MathDB

10.1

Part of 2023 Sharygin Geometry Olympiad

Problems(1)

prove DBC is equal to ACD and BCM

Source: Sharygin Finals 2023 10.1

8/2/2023
Let MM be the midpoint of cathetus ABAB of triangle ABCABC with right angle AA. Point DD lies on the median ANAN of triangle AMCAMC in such a way that the angles ACDACD and BCMBCM are equal. Prove that the angle DBCDBC is also equal to these angles.
geometrySharygin Geometry OlympiadSharygin 2023