MathDB

2017-2018 Spring OMO Problem 28

Source:

April 3, 2018

Problem Statement

In

\triangle ABC

, the incircle

\omega

has center

I

and is tangent to

\overline{CA}

and

Q

at

E

and

F

respectively. The circumcircle of

\triangle{BIC}

meets

\omega

at

P

and

Q

. Lines

AI

and

BC

meet at

D

, and the circumcircle of

\triangle PDQ

meets

\overline{BC}

again at

X

. Suppose that

EF = PQ = 16

and

PX + QX = 17

. Then

BC^2

can be expressed as

\frac mn

, where

m

and

n

are relatively prime positive integers. Find

100m + n

.
Proposed by Ankan Bhattacharya and Michael Ren

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