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Geometric Problem Solving (Circles and Circle Theorems) · CSEC Mathematics

121 past-paper questions on Geometric Problem Solving (Circles and Circle Theorems), part of GEOMETRY AND TRIGONOMETRY, from every CSEC Mathematics paper on Quelpr.

Practise Geometric Problem Solving (Circles and Circle Theorems)
  1. 11(a)(i)2 marks· CSEC Mathematics · 2003 (Specimen) · Paper 2Calculate, giving a reason for your answer, the size of \angle OBD.
  2. 11(a)(ii)2 marks· CSEC Mathematics · 2003 (Specimen) · Paper 2Calculate, giving a reason for your answer, the size of \angle DBC.
  3. 11(a)(iii)2 marks· CSEC Mathematics · 2003 (Specimen) · Paper 2Calculate, giving a reason for your answer, the size of \angle DAB.
  4. 9(a)(i)2 marks· CSEC Mathematics · 2021 · Paper 2Determine the value of angle ECD and give a reason to support your answer.
  5. 9(a)(ii)2 marks· CSEC Mathematics · 2021 · Paper 2Determine the value of angle CEG and give a reason to support your answer.
  6. 9(a)(iii)2 marks· CSEC Mathematics · 2021 · Paper 2Determine the value of angle CGF and give a reason to support your answer.
  7. 9(a)(i)a)1 mark· CSEC Mathematics · 2022 · Paper 2Explain, giving a reason, why angle HJM = 38^\circ.
  8. 9(a)(i)b)1 mark· CSEC Mathematics · 2022 · Paper 2Explain, giving a reason, why angle MJK = 90^\circ.
  9. 9(a)(ii)a)2 marks· CSEC Mathematics · 2022 · Paper 2Determine the value of Angle MLJ. Show detailed working where appropriate.
  10. 9(a)(ii)b)1 mark· CSEC Mathematics · 2022 · Paper 2Determine the value of Angle LJK.
  11. 9(a)(ii)c)1 mark· CSEC Mathematics · 2022 · Paper 2Determine the value of Angle JHM.
  12. Q601 mark · multiple choice· CSEC Mathematics · January 2013 · Paper 1In the diagram, ABC is a triangle in which AD = BD = CD. The angle ABC is
  13. Q541 mark · multiple choice· CSEC Mathematics · January 2014 · Paper 1If O is the centre of the circle, then y^\circ is
  14. Q521 mark · multiple choice· CSEC Mathematics · January 2017 · Paper 1If O is the centre of the circle, then y^\circ is
  15. 9(a)(i)2 marks· Mathematics Q9 9(a)(i)Determine the value of Angle PTR. Show detailed working where necessary and give a reason to support your answer.
  16. 9(a)(i)2 marks· Mathematics Q9 9(a)(i)Calculate the value of ∠DBA. Show detailed working where necessary and give a reason to support your answers.
  17. 9(a)(i)2 marks· Mathematics Q9 9(a)(i)Write down the mathematical names of the straight lines BC and OA.
  18. 9(a)(ii)2 marks· Mathematics Q9 9(a)(ii)Calculate the value of ∠DAC. Show detailed working where necessary and give a reason to support your answers.
  19. 9(a)(ii)2 marks· Mathematics Q9 9(a)(ii)Determine the value of Angle TPQ. Show detailed working where necessary and give a reason to support your answer.
  20. 9(a)(ii)a)2 marks· Mathematics Q9 9(a)(ii)a)Determine the value of angle x. Show detailed working where necessary and give a reason to support your answer.
  21. 9(a)(ii)b)2 marks· Mathematics Q9 9(a)(ii)b)Determine the value of angle y. Show detailed working where necessary and give a reason to support your answer.
  22. 9(a)(iii)2 marks· Mathematics Q9 9(a)(iii)Calculate the value of ∠BCE. Show detailed working where necessary and give a reason to support your answers.
  23. 9(a)(iii)2 marks· Mathematics Q9 9(a)(iii)Determine the value of Obtuse angle POR where O is the centre of the circle. Show detailed working where necessary and give a reason to support your answer.
  24. 9(b)(i)2 marks· Mathematics Q9 9(b)(i)Determine, giving a reason for your answer, ∠ABC
  25. 9(b)(ii)2 marks· Mathematics Q9 9(b)(ii)Determine, giving a reason for your answer, ∠CMB
  26. 9(b)(iii)2 marks· Mathematics Q9 9(b)(iii)Determine, giving a reason for your answer, ∠NCM
  27. 10(a)(i)2 marks· Mathematics Q10 10(a)(i)Calculate, giving reasons for your answer, the measure of ∠FAW.
  28. 10(a)(i)2 marks· Mathematics Q10 10(a)(i)Calculate, giving reasons for EACH step of your answer, the measure of ∠ACD.
  29. 10(a)(i)2 marks· Mathematics Q10 10(a)(i)Calculate, giving a reason for EACH step of your answer, ∠PTR
  30. 10(a)(i)2 marks· Mathematics Q10 10(a)(i)Calculate, giving reasons for your answer, the measure of ∠EHF.
  31. 10(a)(i)2 marks· Mathematics Q10 10(a)(i)Calculate, giving reasons for each step of your answer, the measure of HKL
  32. 10(a)(i)2 marks· Mathematics Q10 10(a)(i)Using the geometrical properties of a circle to give reasons for each step of your answer, determine the measure of ∠SPQ.
  33. 10(a)(i)2 marks· Mathematics Q10 10(a)(i)Calculate, giving reasons for EACH step of your answer, the measure of ∠OGF.
  34. 10(a)(i)2 marks· Mathematics Q10 10(a)(i)Calculate, giving reasons for your answer, the measure of angle XYZ.
  35. 10(a)(i)2 marks· Mathematics Q10 10(a)(i)Calculate, giving reasons for your answer, the measure of ∠ MRQ.
  36. 10(a)(i)2 marks· Mathematics Q10 10(a)(i)Calculate, giving a reason for EACH step of your answer, the measure of: <BOE
  37. 10(a)(i)1 mark· Mathematics Q10 10(a)(i)Calculate, giving reasons for your answer, the measure of <EBF.
  38. 10(a)(ii)3 marks· Mathematics Q10 10(a)(ii)Calculate, giving reasons for EACH step of your answer, the measure of ∠DEF.
  39. 10(a)(ii)2 marks· Mathematics Q10 10(a)(ii)Calculate, giving reasons for your answer, the measure of angle YXZ.
  40. 10(a)(ii)2 marks· Mathematics Q10 10(a)(ii)Calculate, giving reasons for EACH step of your answer, the measure of ∠AED.
  41. 10(a)(ii)2 marks· Mathematics Q10 10(a)(ii)Calculate, giving reasons for your answer, the measure of ∠ PMR.
  42. 10(a)(ii)2 marks· Mathematics Q10 10(a)(ii)Calculate, giving reasons for your answer, the measure of <BOA.
  43. 10(a)(ii)2 marks· Mathematics Q10 10(a)(ii)Calculate, giving a reason for EACH step of your answer, the measure of: <OED
  44. 10(a)(ii)3 marks· Mathematics Q10 10(a)(ii)Using the geometrical properties of a circle to give reasons for each step of your answer, determine the measure of ∠OQS.
  45. 10(a)(ii)2 marks· Mathematics Q10 10(a)(ii)Calculate, giving reasons for each step of your answer, the measure of JÔK
  46. 10(a)(ii)3 marks· Mathematics Q10 10(a)(ii)Calculate, giving a reason for EACH step of your answer, ∠TPR
  47. 10(a)(ii)2 marks· Mathematics Q10 10(a)(ii)Calculate, giving reasons for your answer, the measure of ∠FGH.
  48. 10(a)(ii)2 marks· Mathematics Q10 10(a)(ii)Calculate, giving reasons for your answer, the measure of ∠SKF.
  49. 10(a)(iii)3 marks· Mathematics Q10 10(a)(iii)Calculate, giving a reason for EACH step of your answer, the measure of: <BFE
  50. 10(a)(iii)2 marks· Mathematics Q10 10(a)(iii)Calculate, giving a reason for EACH step of your answer, ∠TSR.
  51. 10(a)(iii)2 marks· Mathematics Q10 10(a)(iii)Calculate, giving reasons for your answer, the measure of ∠JHE.
  52. 10(a)(iii)2 marks· Mathematics Q10 10(a)(iii)Calculate, giving reasons for each step of your answer, the measure of JÂK.
  53. 10(a)(iii)2 marks· Mathematics Q10 10(a)(iii)Calculate, giving reasons for your answer, the measure of <AFB.
  54. 10(a)(iii)3 marks· Mathematics Q10 10(a)(iii)Calculate, giving reasons for your answer, the measure of ∠ PMN.
  55. 10(a)(iii)3 marks· Mathematics Q10 10(a)(iii)Calculate, giving reasons for your answer, the measure of angle OXZ.
  56. 10(a)(iii)2 marks· Mathematics Q10 10(a)(iii)Calculate, giving reasons for EACH step of your answer, the measure of ∠OAC.
  57. 10(a)(iii)2 marks· Mathematics Q10 10(a)(iii)Calculate, giving reasons for your answer, the measure of ∠ASW.
  58. 10(a)(iv)2 marks· Mathematics Q10 10(a)(iv)Calculate, giving reasons for EACH step of your answer, the measure of ∠ABC.
  59. 10(a)(iv)2 marks· Mathematics Q10 10(a)(iv)Calculate, giving reasons for your answer, the measure of <OAF.
  60. 10(a)(iv)2 marks· Mathematics Q10 10(a)(iv)Calculate, giving reasons for your answer, the measure of ∠JGH.
  61. 10(b)(i)2 marks· Mathematics Q10 10(b)(i)Calculate, giving the reason for each step of your answer, the measure of: ∠ADC
  62. 10(b)(i)2 marks· Mathematics Q10 10(b)(i)Calculate, giving the reason for each step of your answer, the measure of: ∠OJH
  63. 10(b)(i)a)2 marks· Mathematics Q10 10(b)(i)a)Calculate, showing working where necessary, the measure of angle OUZ.
  64. 10(b)(i)b)3 marks· Mathematics Q10 10(b)(i)b)Calculate, showing working where necessary, the measure of angle UVY.
  65. 10(b)(i)c)2 marks· Mathematics Q10 10(b)(i)c)Calculate, showing working where necessary, the measure of angle UWO.
  66. 10(b)(ii)2 marks· Mathematics Q10 10(b)(ii)∠ACD
  67. 10(b)(ii)2 marks· Mathematics Q10 10(b)(ii)Calculate, giving the reason for each step of your answer, the measure of: ∠JOG
  68. 10(b)(iii)2 marks· Mathematics Q10 10(b)(iii)∠CAD
  69. 10(b)(iii)2 marks· Mathematics Q10 10(b)(iii)Calculate, giving the reason for each step of your answer, the measure of: ∠JKG
  70. 10(b)(iv)2 marks· Mathematics Q10 10(b)(iv)∠OEA
  71. 10(b)(iv)2 marks· Mathematics Q10 10(b)(iv)Calculate, giving the reason for each step of your answer, the measure of: ∠JLG
  72. 11(a)(i)1 mark· Mathematics Q11 11(a)(i)Calculate angle ABC.
  73. 11(a)(i)2 marks· Mathematics Q11 11(a)(i)Calculate the size of EACH of the following angles, giving reasons for EACH step of your answers: ∠ACB.
  74. 11(a)(i)2 marks· Mathematics Q11 11(a)(i)Calculate, giving a reason for EACH step of your answer, angle WOY.
  75. 11(a)(i)2 marks· Mathematics Q11 11(a)(i)Calculate, giving reasons for your answer, the size of angle PTS.
  76. 11(a)(i)a)2 marks· Mathematics Q11 11(a)(i)a)State, with a reason, why PTQ is a straight line.
  77. 11(a)(i)a)4 marks· Mathematics Q11 11(a)(i)a)Calculate the size of angle VZW, giving reasons for your answer.
  78. 11(a)(i)b)2 marks· Mathematics Q11 11(a)(i)b)State, with a reason, the length PQ.
  79. 11(a)(i)b)4 marks· Mathematics Q11 11(a)(i)b)Calculate the size of angle XYZ, giving reasons for your answer.
  80. 11(a)(i)c)2 marks· Mathematics Q11 11(a)(i)c)State, with a reason, why PS is parallel to QR.
  81. 11(a)(ii)2 marks· Mathematics Q11 11(a)(ii)Calculate, giving reasons for your answer, the size of angle RPQ.
  82. 11(a)(ii)1 mark· Mathematics Q11 11(a)(ii)Calculate angle AOC.
  83. 11(a)(ii)2 marks· Mathematics Q11 11(a)(ii)Calculate, giving a reason for EACH step of your answer, angle OWY.
  84. 11(a)(ii)2 marks· Mathematics Q11 11(a)(ii)Calculate the size of EACH of the following angles, giving reasons for EACH step of your answers: ∠CBD.
  85. 11(a)(iii)1 mark· Mathematics Q11 11(a)(iii)Calculate angle BCD.
  86. 11(a)(iii)2 marks· Mathematics Q11 11(a)(iii)Calculate the size of EACH of the following angles, giving reasons for EACH step of your answers: ∠AED.
  87. 11(a)(iv)1 mark· Mathematics Q11 11(a)(iv)Calculate angle BAC.
  88. 11(a)(v)1 mark· Mathematics Q11 11(a)(v)Calculate angle OAC.
  89. 11(a)(vi)1 mark· Mathematics Q11 11(a)(vi)Calculate angle OAB.
  90. 11(b)(i)8 marks· Mathematics Q11 11(b)(i)Calculate ∠SON.
  91. 11(b)(i)2 marks· Mathematics Q11 11(b)(i)Calculate, giving reasons for your answer, the size of angle OAE.
  92. 11(b)(i)8 marks· Mathematics Q11 11(b)(i)Calculate, giving reasons for each step of your answer, ∠OCE
  93. 11(b)(i)2 marks· Mathematics Q11 11(b)(i)Calculate, giving reasons for your answers, the size of EACH of the following angles: ∠MNL.
  94. 11(b)(ii)8 marks· Mathematics Q11 11(b)(ii)Calculate ∠NMQ.
  95. 11(b)(ii)3 marks· Mathematics Q11 11(b)(ii)Calculate, giving reasons for your answer, the size of angle AOB.
  96. 11(b)(ii)1 mark· Mathematics Q11 11(b)(ii)Calculate, giving reasons for each step of your answer, ∠BAC
  97. 11(b)(ii)3 marks· Mathematics Q11 11(b)(ii)Calculate, giving reasons for your answers, the size of EACH of the following angles: ∠LMO.
  98. 11(b)(iii)2 marks· Mathematics Q11 11(b)(iii)Calculate, giving reasons for your answer, the size of angle ACB.
  99. 11(b)(iii)8 marks· Mathematics Q11 11(b)(iii)Calculate ∠PLN.
  100. 11(b)(iii)1 mark· Mathematics Q11 11(b)(iii)Calculate, giving reasons for each step of your answer, ∠BOC
  101. 11(b)(iv)8 marks· Mathematics Q11 11(b)(iv)Calculate ∠SNM.
  102. 11(b)(iv)2 marks· Mathematics Q11 11(b)(iv)Calculate, giving reasons for your answer, the size of angle ADB.
  103. 11(b)(iv)1 mark· Mathematics Q11 11(b)(iv)Calculate, giving reasons for each step of your answer, ∠BDC.
  104. 12(a)(i)2 marks· Mathematics Q12 12(a)(i)Calculate, stating reasons for your answers, the size of the following angles: KLN.
  105. 12(a)(i)2 marks· Mathematics Q12 12(a)(i)Calculate, giving reasons for your answer, the measure of angle GFH.
  106. 12(a)(i)8 marks· Mathematics Q12 12(a)(i)Calculate, giving reasons for your answers, the size of angle BEO.
  107. 12(a)(ii)3 marks· Mathematics Q12 12(a)(ii)Calculate, giving reasons for your answer, the measure of angle GDE.
  108. 12(a)(ii)3 marks· Mathematics Q12 12(a)(ii)Calculate, stating reasons for your answers, the size of the following angles: NKL.
  109. 12(a)(ii)8 marks· Mathematics Q12 12(a)(ii)Calculate, giving reasons for your answers, the size of angle BCE.
  110. 12(a)(iii)2 marks· Mathematics Q12 12(a)(iii)Calculate, stating reasons for your answers, the size of the following angles: LMN.
  111. 12(a)(iii)2 marks· Mathematics Q12 12(a)(iii)Calculate, giving reasons for your answer, the measure of angle DEF.
  112. 12(a)(iii)8 marks· Mathematics Q12 12(a)(iii)Calculate, giving reasons for your answers, the size of angle BAE.
  113. 12(a)(iv)8 marks· Mathematics Q12 12(a)(iv)Calculate, giving reasons for your answers, the size of angle BOE.
  114. 12(b)(i)2 marks· Mathematics Q12 12(b)(i)State why LMNS is a rectangle.
  115. 12(b)(ii)a)6 marks· Mathematics Q12 12(b)(ii)a)Calculate the size of angle LNS.
  116. 12(b)(ii)b)6 marks· Mathematics Q12 12(b)(ii)b)Calculate the size of angle LKS.
  117. 12(b)(ii)c)6 marks· Mathematics Q12 12(b)(ii)c)Calculate the size of angle LOS.
  118. 12(b)a)9 marks· Mathematics Q12 12(b)a)Calculate the size of angle TPQ, giving reasons for your answer.
  119. 12(b)b)1 mark· Mathematics Q12 12(b)b)Calculate the size of angle MTQ, giving reasons for your answer.
  120. 12(b)c)1 mark· Mathematics Q12 12(b)c)Calculate the size of angle TQS, giving reasons for your answer.
  121. 12(b)d)1 mark· Mathematics Q12 12(b)d)Calculate the size of angle SRQ, giving reasons for your answer.

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