Geometry Problem
Level: Mathematics Education, High School, Honors Geometry, College.
Click the figure below to see the problem 720 details.
Monday, January 23, 2012
Problem 720: Excenter, Intersecting Circles, Angle, Measurement
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Let CO'D cut the circle (O') at E.
ReplyDeleteBy the result of Problem 719,
E is the incentre of ∆ABC
Observing that ED is a diameter of circle (O'),
it follows that AD ⊥ AE, implying that
AD is the external bisector of ∠CAB.
By symmetry,
BD is the exteral bisector of ∠CBA.
Hence D is an excentre of ∆ABC