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Geometry Mathley 10.1 right angle wanted

Source:

June 7, 2020

geometryright angleincirclecircumcircletangent circles

Problem Statement

Let

ABC

be a triangle with two angles

B,C

not having the same measure,

I

be its incircle,

(O)

its circumcircle. Circle

(O_b)

touches

BA,BC

and is internally tangent to

(O)

at

B_1

. Circle

(O_c)

touches

CA,CB

and is internally tangent to

(O)

at

C_1

. Let

S

be the intersection of

BC

and

B_1C_1

. Prove that

\angle AIS = 90^o

.
Nguyễn Minh Hà

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