MathDB

perpendicular common tangents to intersecting circles

Source: Canada Rep&ecirc;chage 2023/3 CMOQR

March 25, 2024

geometrycommon tangents

Problem Statement

Let circles

\Gamma_1

and

\Gamma_2

have radii

r_1

and

r_2

, respectively. Assume that

r_1 < r_2

. Let

T

be an intersection point of

\Gamma_1

and

\Gamma_2

, and let

S

be the intersection of the common external tangents of

\Gamma_1

and

\Gamma_2

. If it is given that the tangents to

\Gamma_1

and

\Gamma_2

T

are perpendicular, determine the length of

ST

in terms of

r_1

and

r_2