MathDB

17

Part of 1982 IMO Shortlist

Problems(1)

Right triangles

Source: IMO LongList 1982 - P54

9/10/2010
The right triangles ABCABC and AB1C1AB_1C_1 are similar and have opposite orientation. The right angles are at CC and C1C_1, and we also have ∠CAB=∠C1AB1 \angle CAB = \angle C_1AB_1. Let MM be the point of intersection of the lines BC1BC_1 and B1CB_1C. Prove that if the lines AMAM and CC1CC_1 exist, they are perpendicular.
geometryTriangleright trianglesimilar trianglesperpendicularIMO ShortlistIMO Longlist