MathDB

Let

k

be a circle with diameter

AB

. A point

C

is chosen inside the segment

AB

and a point

D

is chosen on

k

such that

BCD

is an acute-angled triangle, with circumcentre denoted by

O

. Let

E

be the intersection of the circle

k

and the line

BO

(different from

B

). Show that the triangles

BCD

and

ECA

are similar.

Problem Statement