MathDB

10

Part of 2023 Sharygin Geometry Olympiad

Problems(1)

angle bisector circumcircle tangency

Source: Sharygin 2023 - P10 (Grade-8-9)

3/4/2023
Altitudes BEBE and CFCF of an acute-angled triangle ABCABC meet at point HH. The perpendicular from HH to EFEF meets the line ℓ\ell passing through AA and parallel to BCBC at point PP. The bisectors of two angles between ℓ\ell and HPHP meet BCBC at points SS and TT. Prove that the circumcircles of triangles ABCABC and PSTPST are tangent.
geometryangle bisectortangent circlesSharygin Geometry OlympiadSharygin 2023