SOLUTION: Hello! The problem I have is a triangle inscribed in a circle, this is what I have given: Given: m∠A = 53°, BC = 25 I need to find the radius: Find: R (OC = OB

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Question 1132644: Hello!
The problem I have is a triangle inscribed in a circle, this is what I have given:
Given: m∠A = 53°, BC = 25

I need to find the radius:
Find: R (OC = OB = OA)
You have points A, B, and C on a circle which form a triangle, and the circle has point O as the center point.
I tried making a perpendicular line from point B to line AC, but we don't know if that is possible to split the given triangle into two equal triangles. I am not sure how else I can solve this problem.
Thanks for helping!

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Angle A is an inscribed angle. The measure of an inscribed angle is one-half of the measure of the subtended arc, hence arc BC measures 106 degrees. And since the measure of an arc is equal to the measure of the central angle, angle BOC measures 106 degrees also. Locate the midpoint of segment BC and label that point D. The perpendicular bisector of any chord passes through the center of the circle. You now have a right triangle ODB with angle BOD measuring one half of angle BOC, namely 53 degrees, a radius of the circle as the hypotenuse, and the leg opposite angle BOD that measures 12.5 units.

Since ,

You can do your own arithmetic.

John

My calculator said it, I believe it, that settles it