+367 A circle centered at O is circumscribed about Triangle ABC as follows:
https://latex.artofproblemsolving.com/e/3/3/e3327b08d906e6cc74d5f9f0232a3016dea5197b.png
What is the measure of BAC?
I think this question was answered before but the person who answered it didn't explain how they got their answer.
+129852 Since O is the center......the measure of angle COA = (360 - 100 - 110) = 150
And triangle COA is isosceles with OC = OA
So angle OAC = (180 - 150) /2 = 15
And triangle BOA is also isosceles with OB = OA
So angle OAB = ( 180 - 110) / 2 = 35
So angle BAC = angle OAB + OAC = 35 + 15 = 50°
Another (easier) way to see this is to note that central angle BOC =100
And angle BAC is an inscribed angle which subtends the same arc as BOC
So...its measure = (1/2) of BOC = (100) / 2 = 50°
