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Length of BC must be $(12+9\sqrt{15})/5$

Source: Bstat-Bmath 2017: Problem 2

May 14, 2017

geometry

Problem Statement

Consider a circle of radius

6

. Let

B,C,D

and

E

be points on the circle such that

BD

and

CE

, when extended, intersect at

A

. If

AD

and

AE

have length

5

and

4

respectively, and

DBC

is a right angle, then show that the length of

BC

is

\frac{12+9\sqrt{15}}{5}

.

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