MathDB

Accuracy P10

Source:

October 16, 2021

MOAA 2021Accuracy

Problem Statement

In

\triangle ABC

, let

X

and

Y

be points on segment

BC

such that

AX=XB=20

and

AY=YC=21

. Let

J

be the

A

-excenter of triangle

m

. Given that

J

lies on the circumcircle of

\triangle ABC

, the length of

BC

can be expressed as

\frac{m}{n}

for relatively prime positive integers

m

and

n

. Compute

m+n

.
Proposed by Andrew Wen

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