MathDB
Altitude and Median from two vertices

Source: Saint Petersburg 2017

August 18, 2017
geometrycircumcircle

Problem Statement

In acute-angled triangle ABCABC, the height AHAH and median BMBM were drawn. Point DD lies on the circumcircle of triangle BHMBHM such that ADBMAD \parallel BM and B,DB, D are on opposite sides of line ACAC. Prove that BC=BDBC=BD.