Quelpr
1 markCo-ordinate Geometry

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

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.

Write down the size of angle PQR.

The mark scheme is shown once you've answered.

Practise this question

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)(ii)Calculate, in terms of r, the area of triangle PQR.[2 marks]
  3. 1(b)(iii)Write down the size of angle PSQ.[1 mark]
  4. 1(b)(iv)By considering triangle PSR, or otherwise, show that r/(r+α) = √3/2.[2 marks]
  5. 1(b)(v)Calculate, in terms of r, the area of the shaded region.[6 marks]

More practice: the rest of this paper · more Co-ordinate Geometry questions · all CAPE Pure Mathematics Unit 1 past papers