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

Labels:
angle,
excenter,
intersecting circles,
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