MathDB

2019 MOAA Team P5

Source:

January 23, 2022

geometryteam2019

Problem Statement

Let

ABC

be a triangle with

AB = AC = 10

and

BC = 12

. Define

\overline{BC}

as the line through

A

perpendicular to

\overline{AB}

. Similarly,

\ell_B

is the line through

B

perpendicular to

\overline{BC}

and

\ell_C

is the line through

C

perpendicular to

\overline{CA}

. These three lines

\ell_A, \ell_B, \ell_C

form a triangle with perimeter

m/n

for relatively prime positive integers

m

and

n

. Find

m + n

.

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