ISL 2007 G1

In triangle $A B C$ , the angle bisector at vertex $C$ intersects the circumcircle and the perpendicular bisectors of sides $B C$ and $C A$ at points $R, P$ , and $Q$ , respectively. The midpoints of $B C$ and $C A$ are $S$ and $T$ , respectively. Prove that triangles $R Q T$ and $R P S$ have the same area. (Czech Republic)

Dataset text NuminaMath olympiads. Quoted with source.

Official text: IMO 2007 Shortlist booklet, page 40.

Solutions

Official solution Solution 1 by the IMO Problem Selection Committee

The terms of the source let olymmath link to this solution but not copy it. Read the solution (IMO official site).

Locator isl/2007/g1 · Tag ZQJGWWPCNW · Edit this page on GitHub · Keys: j next, k previous