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\\ tangents from points A,B of a circle with center C, where <ACB=90^o

Source: Netherlands - Dutch NMO 1962 p1

January 31, 2023

geometryTangentsparallelconstructionright triangle

Problem Statement

Given a triangle

ABC

with

\angle C = 90^o

. a) Construct the circle with center

C

, so that one of the tangents from

A

to that circle is parallel to one of the tangents from

B

to that circle. b) A circle with center

C

has two parallel tangents passing through A and go respectively. If

AC = b

and

BC = a

, express the radius of the circle in terms of

a

and

b