MathDB

APMC 1997

Source:

February 25, 2011

geometryrectangleparallelogramgeometry unsolved

Problem Statement

Let

P

be the intersection of lines

l_1

and

l_2

. Let

S_1

and

S_2

be two circles externally tangent at

P

and both tangent to

l_1

, and let

T_1

and

T_2

be two circles externally tangent at

P

and both tangent to

l_2

. Let

A

be the second intersection of

S_1

and

T_1, B

that of

S_1

and

T_2, C

that of

S_2

and

T_1

, and

D

that of

S_2

and

T_2

. Show that the points

A,B,C,D

are concyclic if and only if

l_1

and

l_2

are perpendicular.

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