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
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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.