2

Part of 2017 ISI Entrance Examination

Problems(1)

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

Source: Bstat-Bmath 2017: Problem 2

Consider a circle of radius

6

B,C,D

E

be points on the circle such that

BD

CE

, when extended, intersect at

A

AD

AE

5

4

respectively, and

DBC

is a right angle, then show that the length of

BC

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