MathDB

Math Prize 2021 Problem 8

Source:

September 19, 2021

Math Prize for Girls

Problem Statement

In

E

, let point

D

be on

\overline{BC}

such that the perimeters of

\triangle ADB

and

\triangle ADC

are equal. Let point

E

be on

\overline{AC}

such that the perimeters of

\triangle BEA

and

\triangle BEC

are equal. Let point

F

be the intersection of

\overline{AB}

with the line that passes through

C

and the intersection of

\overline{AD}

and

\overline{BE}

. Given that

BD = 10

,

CD = 2

, and

BF/FA = 3

, what is the perimeter of

\triangle ABC

?

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