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an apollonius circle construction, PPC in swiss NMO

Source: Switzerland - Swiss ΜΟ 2015 p4

July 15, 2020

geometry

Problem Statement

Given a circle

k

and two points

A

and

B

outside the circle. Specify how to can construct a circle with a compass and ruler, so that

A

and

B

lie on that circle and that circle is tangent to

k