MathDB

2021-22 Winter Team #7

Source:

April 17, 2022

geometry

Problem Statement

Let

ABC

be a triangle with

AB = 5

,

BC = 6

, and

CA = 7

. Denote

\Gamma

the incircle of

ABC

, let

I

be the center of

\Gamma

. The circumcircle of

BIC

intersects

\Gamma

at

X_1

and

X_2

. The circumcircle of

CIA

intersects

\Gamma

at

Y_1

and

Y_2

. The circumcircle of

AIB

intersects

\Gamma

at

Z_1

and

Z_2

. The area of the triangle determined by

\overline{X_1X_2}

,

\overline{Y_1Y_2}

, and

\overline{Z_1Z_2}

equals

\frac{m \sqrt{p}}{n}

for positive integers

m, n

, and

p

, where

m

and

n

are relatively prime and

p

is squarefree. Compute

m+n+ p

.

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