MathDB

2013-2014 Fall OMO #21

Source:

October 30, 2013

Online Math Opengeometryincentertrigonometryinradiusanalytic geometrycircumcircle

Problem Statement

Let

ABC

be a triangle with

AB = 5

,

AC = 8

, and

BC = 7

. Let

D

be on side

AC

such that

AD = 5

and

CD = 3

. Let

I

be the incenter of triangle

ABC

and

E

be the intersection of the perpendicular bisectors of

\overline{ID}

and

\overline{BC}

. Suppose

DE = \frac{a\sqrt{b}}{c}

where

a

and

c

are relatively prime positive integers, and

b

is a positive integer not divisible by the square of any prime. Find

a+b+c

.
Proposed by Ray Li

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