MathDB

RS tangent to mixtilinear incircle wanted, isosceles ABC

Source: 2021 Cono Sur Shortlist G7 https://artofproblemsolving.com/community/c1088686_cono_sur_shortlist__geometry

October 31, 2022

geometrymixtilinear incircletangentisosceles

Problem Statement

Given an triangle

ABC

isosceles at the vertex

A

, let

P

and

Q

be the touchpoints with

AB

and

AC

, respectively with the circle

T

, which is tangent to both and is internally tangent to the circumcircle of

ABC

. Let

R

and

S

be the points of the circumscribed circle of

ABC

such that

AP = AR = AS

. Prove that

RS

is tangent to

T