MathDB

3

Part of 2024 Mexican Girls' Contest

Problems(1)

altitude and circumcircles

Source: 3rd National Women´s Contest of Mexican Mathematics Olympiad 2024 , level 1+2 p3

6/13/2024
Let ABC ABC be a triangle and D D the foot of the altitude from A A . Let M M be a point such that MB=MC MB = MC . Let E E and F F be the intersections of the circumcircle of BMD BMD and CMD CMD with AD AD . Let G G and H H be the intersections of MB MB and MC MC with AD AD . Prove that EG=FH EG = FH .
geometryMexicocircumcircle