MathDB

Team Round P12

Source:

October 16, 2021

MOAA 2021team

Problem Statement

Let

\triangle ABC

have

AB=9

and

AC=10

. A semicircle is inscribed in

\triangle ABC

with its center on segment

BC

such that it is tangent

AB

at point

D

and

AC

at point

E

. If

AD=2DB

and

r

is the radius of the semicircle,

r^2

can be expressed as

\frac{m}{n}

for relatively prime positive integers

m

and

n

. Compute

m+n

.
Proposed by Andy Xu

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