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10.1

Part of Geometry Mathley 2011-12

Problems(1)

Geometry Mathley 10.1 right angle wanted

Source:

6/7/2020
Let ABCABC be a triangle with two angles B,CB,C not having the same measure, II be its incircle, (O)(O) its circumcircle. Circle (Ob)(O_b) touches BA,BCBA,BC and is internally tangent to (O)(O) at B1B_1. Circle (Oc)(O_c) touches CA,CBCA,CB and is internally tangent to (O)(O) at C1C_1. Let SS be the intersection of BCBC and B1C1B_1C_1. Prove that ∠AIS=90o\angle AIS = 90^o.
Nguyễn Minh Hà
geometryright angleincirclecircumcircletangent circles