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0433 geometry 4th edition Round 3 p3

Source:

May 7, 2021

geometry4th edition

Problem Statement

Let

ABC

be a triangle, and let

C

be its circumcircle. Let

T

be the circle tangent to

AB, AC

and

C

internally in the points

F, E

and

D

respectively. Let

P, Q

be the intersection points between the line

EF

and the lines

DB

and

DC

respectively. Prove that if

DP = DQ

then the triangle

ABC

is isosceles.

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