MathDB

Gunga P23

Source:

October 16, 2021

MOAA 2021Gunga

Problem Statement

Let

P

be a point chosen on the interior of side

\overline{BC}

of triangle

\triangle ABC

with side lengths

\overline{AB} = 10, \overline{BC} = 10, \overline{AC} = 12

. If

X

and

Y

are the feet of the perpendiculars from

P

to the sides

AB

and

AC

, then the minimum possible value of

PX^2 + PY^2

can be expressed as

\frac{m}{n}

where

m

and

n

are relatively prime positive integers. Find

m+n

.
Proposed by Andrew Wen

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