Geometry Problem

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the problem 719 details.

## Monday, January 23, 2012

### Problem 719: Incenter, Intersecting Circles, Angle, Measurement

Labels:
angle,
incenter,
intersecting circles,
measurement,
midpoint

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Equal arcs AO’, BO’ of circle (O) subtend equal angles at the circumference.

ReplyDeleteSo ∠ACO’ = ∠BCO’ and so

CD bisects ∠ACB …… (i)

Next ∠DAB =(1/2)∠DO’B referred to circle(O’)

=(1/2)∠CO’B =(1/2)∠CAB referred to circle(O) and so

AD bisects ∠CAB …… (ii)

From (i) and (ii), it follows that

D is the incentre of ∆ABC.