MathDB

P16

Part of 2017 Sharygin Geometry Olympiad

Problems(1)

points definded by projections of intersections of tangents on sides

Source: Sharygin Geometry Olympiad 2017 First Round P16 grades 9-11

7/22/2018
The tangents to the circumcircle of triangle ABCABC at AA and BB meet at point DD. The circle passing through the projections of DD to BC,CA,ABBC, CA, AB, meet ABAB for the second time at point C′C'. Points A′,B′A', B' are defined similarly. Prove that AA′,BB′,CC′AA', BB', CC' concur.
geometryconcurrencyconcurrenttangent