MathDB

The tangents at

B

and

A

to the circumcircle of an acute angled triangle

ABC

meet the tangent at

C

T

and

U

respectively.

AT

meets

BC

P

, and

Q

is the midpoint of

AP

;

BU

meets

CA

R

, and

S

is the midpoint of

BR

. Prove that

\angle ABQ=\angle BAS

. Determine, in terms of ratios of side lengths, the triangles for which this angle is a maximum.

Problem Statement