IMC 2009 Q17
17. \(PQR\) is a triangle and \(S\) is a point on \(QR\).
\(QP = QR = 9\) cm and \(PR = PS = 6\) cm.
What is the length of \(SR\)?
- A 1cm
- B 2cm
- C 3cm
- D 4cm
- E 5cm
Intermediate Mathematical Challenge 2009, Question 17. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 4cm
Triangles \(PRS\) and \(QPR\) are similar because: \(\angle PSR = \angle QRP\) (since \(PR = PS\)) and \(\angle PRS = \angle QPR\) (since \(QP = QR\)). Hence \(\dfrac{SR}{RP} = \dfrac{RP}{PQ}\), that is \(\dfrac{SR}{6} = \dfrac{6}{9}\), that is \(SR = 4\).
Solution © UK Mathematics Trust, from the IMC 2009 solutions.