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another circle which passes through E and F

Source: China TST 1999, problem 4

May 22, 2005

geometryperpendicular bisectorpower of a pointradical axisgeometry unsolved

Problem Statement

A circle is tangential to sides

AB

and

AD

of convex quadrilateral

ABCD

G

and

H

respectively, and cuts diagonal

AC

E

and

F

. What are the necessary and sufficient conditions such that there exists another circle which passes through

E

and

F

, and is tangential to

DA

and

DC

extended?