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Geo #3 EQuals FReak out

Source: 2018 USAJMO #3

April 18, 2018

USAJMO2018 USAJMO Problem 3geometrygeometry solvedorthocentereasyevan orz

Problem Statement

Let

ABCD

be a quadrilateral inscribed in circle

\omega

with

\overline{AC} \perp \overline{BD}

. Let

E

and

F

be the reflections of

D

over lines

BA

and

BC

, respectively, and let

P

be the intersection of lines

BD

and

EF

. Suppose that the circumcircle of

\triangle EPD

meets

\omega

at

D

and

Q

, and the circumcircle of

\triangle FPD

meets

\omega

at

D

and

R

. Show that

EQ = FR

.

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