MathDB

angle bisector circumcircle tangency

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

March 4, 2023

geometryangle bisectortangent circlesSharygin Geometry OlympiadSharygin 2023

Problem Statement

Altitudes

BE

and

CF

of an acute-angled triangle

ABC

meet at point

H

. The perpendicular from

H

EF

meets the line

\ell

passing through

A

and parallel to

BC

at point

P

. The bisectors of two angles between

\ell

and

HP

meet

BC

at points

S

and

T

. Prove that the circumcircles of triangles

ABC

and

PST

are tangent.