Question 1132646: Hello!
I have a problem that has a triangle inscribed in a circle with points A, B, and C, and center of the circle, O.
This is what I have given:
Given: m∠A = 53°, BC = 25
I need to find the radius of the circle:
Find: R (OC = OB = OA)
I tried drawing a perpendicular line from point B (on top) to line AC (bottom), but I can't solve it that way because we have no way of knowing that It can split the given triangle into 2 equal parts. I'm not sure how to solve this problem and need help.
Thanks for helping!
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
Angle A (i.e., angle BAC) is an inscribed angle with measure 53 degrees. Angle BOC is a central angle cutting off the same arc, so its measure is 106 degrees.
BC is a chord of the circle. The radius OD perpendicular to BC at E is the perpendicular bisector of BC.
That makes triangles BOE and COE congruent; that makes angle BOE 53 degrees.
In triangle BOE, radius OB is the length you are looking for; BE is 12.5 (half the length of the chord); and angle BOE is 53 degrees.
Use the appropriate trig function using those numbers to determine the radius.
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