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2 circles tangent internally to a third circle and to one secant of that circle

Source: Rioplatense Olympiad 1997 level 3 P4

September 4, 2018

geometrytangent circles

Problem Statement

Circles

c_1

and

c_2

are tangent internally to circle

c

at points

A

and

B

, respectively, as seen in the figure. The inner tangent common to

c_1

and

c_2

touches these circles in

P

and

Q

, respectively. Show that the

AP

and

BQ

lines intersect the circle

c

at diametrically opposite points. https://cdn.artofproblemsolving.com/attachments/0/a/9490a4d7ba2038e490a858b14ba21d07377c5d.gif