MathDB

2023 Spring LMT Team #9

Source:

August 10, 2023

geometry

Problem Statement

In

\vartriangle ABC

,

B

,

BC = 14,

and

C A = 15

. Let

E

and

F

be the feet of the altitudes from

B

onto

C A

, and

C

onto

AB

, respectively. A line

\ell

is parallel to

EF

and tangent to the circumcircle of

ABC

on minor arc

BC

. Let

X

and

Y

be the intersections of

\ell

with

AB

and

AC

respectively. Find

X Y

.

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