MathDB

Two circumferences, with the distance

d

between centres, intersect in points

P

and

Q

. Two lines are drawn through the point

A

on the first circumference (

Q\ne A\ne P

) and points

P

and

Q

. They intersect the second circumference in the points

B

and

C

.
a) Prove that the radius of the circle, circumscribed around the triangle

ABC

, equals

d

.
b) Describe the set of the new circle's centres, if thepoint

A

moves along all the first circumference.

Problem Statement