MathDB

3 circles tangent internally to circumcircle and sides ABC

Source: JBMO Shortlist 2004

October 13, 2017

geometrycircumcircleJBMO

Problem Statement

Let

ABC

be a triangle inscribed in circle

C

. Circles

C_1, C_2, C_3

are tangent internally with circle

C

in

A_1, B_1, C_1

and tangent to sides

[BC], [CA], [AB]

in points

A_2, B_2, C_2

respectively, so that

A, A_1

are on one side of

C_1C_2

and so on. Lines

A_1A_2, B_1B_2

and

M = BB’ \cap CC’

intersect the circle

C

for second time at points

A’,B’

and

C’

, respectively. If

M = BB’ \cap CC’

, prove that

m (\angle MAA’) = 90^\circ

.

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