MathDB

10.5

Part of 2022 Sharygin Geometry Olympiad

Problems(1)

common ext.tangents of MDP and MPE meet on midline of triangle ABC

Source: Sharygin Finals 2022 10.5

10/26/2022
LetAB AB and ACAC be the tangents from a point AA to a circle Ω \Omega. Let MM be the midpoint of BCBC and PP be an arbitrary point on this segment. A line APAP meets Ω \Omega at points DD and EE. Prove that the common external tangents to circles MDPMDP and MPEMPE meet on the midline of triangle ABCABC.
geometryconcurrencycommon tangents