MathDB

Let

ABC

be a triangle. An arbitrary circle which passes through the points

B,C

intersects the sides

AC,AB

for the second time in

D,E

respectively. The line

BD

intersects the circumcircle of the triangle

AEC

P{}

and

Q{}

and the line

CE

intersects the circumcircle of the triangle

ABD

R{}

and

S{}

such that

P{}

is situated on the segment

BD{}

and

R{}

lies on the segment

CE.

Prove that:
[*]The points

P,Q,R

and

S{}

are concyclic. [*]The triangle

APQ

is isosceles.
Petru Braica

Problem Statement