MathDB

Problem 3 of Second round - Constructing two points on given circles

Source: I International Festival of Young Mathematicians Sozopol 2010, Theme for 10-12 grade

December 14, 2019

geometryconstructionconstructive geometry

Problem Statement

Two circles are intersecting in points

P

and

Q

. Construct two points

A

and

B

on these circles so that

P\in AB

and the product

AP.PB

is maximal.