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2 marksCo-ordinate Geometry

CAPE Pure Mathematics Unit 1 · May/June 1999 · Paper 2 · Question 1(b)(iv)

A company logo consists of three externally touching circles, each of radius r, with centers P, Q, R. A fourth circle, with center S and radius a, touches each of the three large circles.

By considering triangle PSR, or otherwise, show that r/(r+α) = √3/2.

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Other parts of this question

  1. 1(a)Solve the simultaneous equations: (x - 2)² + (y+2)² = 4, y+x-2=0.[8 marks]
  2. 1(b)(i)Write down the size of angle PQR.[1 mark]
  3. 1(b)(ii)Calculate, in terms of r, the area of triangle PQR.[2 marks]
  4. 1(b)(iii)Write down the size of angle PSQ.[1 mark]
  5. 1(b)(v)Calculate, in terms of r, the area of the shaded region.[6 marks]

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