IMC 2010 Q6
6. In triangle \(PQR\), \(S\) is a point on \(QR\) such that \(QS = SP = PR\) and \(\angle QPS = 20\)°. What is the size of \(\angle PRS\)?
- A 20°
- B 35°
- C 40°
- D 55°
- E 60°
Intermediate Mathematical Challenge 2010, Question 6. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 40°
Triangle \(PQS\) is isosceles with \(PS = QS\) so \(\angle PQS = \angle SPQ = 20^\circ\). Therefore \(\angle PSR\) = 20° + 20° = 40° (exterior angle theorem). Triangle \(PSR\) is also isosceles, with \(PS = PR\), so \(\angle PRS = \angle PSR = 40^\circ\).
Solution © UK Mathematics Trust, from the IMC 2010 solutions.