MathDB

In rectangle

ABCD

, points

E

and

F

are on sides

\overline{BC}

and

\overline{AD}

, respectively. Two congruent semicircles are drawn with centers

E

and

F

such that they both lie entirely on or inside the rectangle, the semicircle with center

E

passes through

C

, and the semicircle with center

F

passes through

A

. Given that

AB=8

CE=5

, and the semicircles are tangent, find the length

BC

.
Proposed by Ada Tsui

Problem Statement