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Concurrency of two common external tangents

Source: Iran TST 2013-First exam-2nd day-P6

April 19, 2013

functiongeometryIranIranian TST

Problem Statement

Points

A, B, C

and

D

lie on line

l

in this order. Two circular arcs

C_1

and

C_2

, which both lie on one side of line

l

, pass through points

A

and

B

and two circular arcs

C_3

and

C_4

pass through points

C

and

D

such that

C_1

is tangent to

C_3

and

C_2

is tangent to

C_4

. Prove that the common external tangent of

C_2

and

C_3

and the common external tangent of

C_1

and

C_4

meet each other on line

l

.
Proposed by Ali Khezeli

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