MathDB

5

Part of 1990 Irish Math Olympiad

Problems(1)

Right Triangle

Source: 1990 IrMO Paper 1 Problem 5

9/30/2017
Let ABCABC be a right-angled triangle with right-angle at AA. Let XX be the foot of the perpendicular from AA to BCBC, and YY the mid-point of XCXC. Let ABAB be extended to DD so that ∣AB∣=∣BD∣|AB|=|BD|. Prove that DXDX is perpendicular to AYAY.
geometry