MathDB

2014-2015 Spring OMO #5

Source:

April 14, 2015

Online Math Open

Problem Statement

Let

ABC

be an isosceles triangle with

\angle A = 90^{\circ}

. Points

D

and

E

are selected on sides

AB

and

AC

, and points

X

and

Y

are the feet of the altitudes from

D

and

E

to side

BC

. Given that

AD = 48\sqrt2

and

AE = 52\sqrt2

, compute

XY

.
Proposed by Evan Chen

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