MathDB

Locus of XZ \cap ZT

Source: 9.7 of XX Geometrical Olympiad in honour of I.F.Sharygin

August 6, 2024

geometrygeo

Problem Statement

Let

P

and

Q

be arbitrary points on the side

BC

of triangle ABC such that

BP = CQ

. The common points of segments

AP

and

AQ

with the incircle form a quadrilateral

XYZT

. Find the locus of common points of diagonals of such quadrilaterals.