MathDB

6

Part of 1996 Mexico National Olympiad

Problems(1)

collinearity as a result of perpendicularity and equality

Source: Mexican Mathematical Olympiad 1996 OMM P6

7/28/2018
In a triangle ABCABC with AB<BC<ACAB < BC < AC, points A′,B′,C′A' ,B' ,C' are such that AA′⊥BCAA' \perp BC and AA′=BC,BB′⊥CAAA' = BC, BB' \perp CA and BB′=CABB'=CA, and CC′⊥ABCC' \perp AB and CC′=ABCC'= AB, as shown on the picture. Suppose that ∠AC′B\angle AC'B is a right angle. Prove that the points A′,B′,C′A',B' ,C' are collinear.
geometryperpendicularitycollinearity