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Geometry Mathley 6.3 tangent circles

Source:

June 7, 2020

tangent circlescirclesgeometry

Problem Statement

Let

AB

be an arbitrary chord of the circle

(O)

. Two circles

(X)

and

(Y )

are on the same side of the chord

AB

such that they are both internally tangent to

(O)

and they are tangent to

AB

at

C,D

respectively,

C

is between

A

and

D

. Let

H

be the intersection of

XY

and

AB, M

the midpoint of arc

AB

not containing

X

and

Y

. Let

HM

meet

(O)

again at

I

. Let

IX, IY

intersect

AB

again at

K, J

. Prove that the circumcircle of triangle

IKJ

is tangent to

(O)

.
Nguyễn Văn Linh

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