MathDB

Maximize (AP_1)(AP_2)

Source: Sharygin Finals 2022 9.2

July 31, 2022

geometry

Problem Statement

Let circles

s_1

and

s_2

meet at points

A

and

B

. Consider all lines passing through

A

and meeting the circles for the second time at points

P_1

and

P_2

respectively. Construct by a compass and a ruler a line such that

AP_1.AP_2

is maximal.