MathDB

Sad Geometry

Source: 2018 China TST Day 3 Q 1

January 21, 2018

geometry

Problem Statement

Given a triangle

ABC

.

D

is a moving point on the edge

BC

. Point

E

and Point

F

are on the edge

AB

and

AC

, respectively, such that

BE=CD

and

CF=BD

. The circumcircle of

\triangle BDE

and

\triangle CDF

intersects at another point

P

other than

D

. Prove that there exists a fixed point

Q

, such that the length of

QP

is constant.

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