MathDB

BMT 2021 Guts Round p22

Source:

October 7, 2022

geometry

Problem Statement

In

\vartriangle ABC

, let

D

and

E

be points on the angle bisector of

\angle BAC

such that

\angle ABD = \angle ACE =90^o

. Furthermore, let

F

be the intersection of

AE

and

BC

, and let

O

be the circumcenter of

\vartriangle AF C

. If

\frac{AB}{AC} =\frac{3}{4}

,

AE = 40

, and

BD

bisects

EF

, compute the perpendicular distance from

A

to

OF

.

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