If the radius of the circle circumscribing a triangle is the same as

Question

If the radius of the circle circumscribing a triangle is the same as one of the sides of an acute angled triangle, then what is the measure of the angle opposite the side?

A. 30
B. 45
C. 60
D. 90
E. 15

Kudos for a correct  solution .

ENGRTOMBA2018 · Accepted Answer

Refer to the attached picture. O is the center of the circle and r is the radius such that  OA=OB = AB = r .

Triangle OAB is an equilateral triangle with  \angle{AOB} = 60

Now minor arc AB subtends an angle of 60 at the center and thus it will subtend 60/2 = 30 at the circumference, making  \angle{ACB} = 30 . Thus A is the correct answer.

gopal1987 · Answer

Why have you assumed an equilateral triangle? 
Or is it a theory necessary for solving this problem?

Thanks

ENGRTOMBA2018 · Answer

I have not assumed anything.

It is given that radius of the circle is equal to the side of the triangle.

GMATinsight · Answer

Property: Angle subtended by any segment of the circle at the centre is twice the angle subtended by same segment on the circumference of the circle.

Answer: option A

gopal1987 · Answer

Understood. Thanks a lot Bunuel

VenoMfTw · Answer

IMO: A 11.jpg Above is the diagram AOB is equilateral triangle. Thus ∠AOB = 60 Angle Subtended by a chord at center = 2* Angle subtended by the same chord on the circumference of the circle ∠AOB = 2* ∠ACB Thus ∠ACB = 30 ( Opposite to the side AB which is equal to the radius of the circle)

TarunKumar1234 · Answer

If one of the side is Radius then other sides of a new triangle, having one point O, will be equilateral triangle. So, opposite angle = 60/2 = 30 It is A.

bumpbot · Answer

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If the radius of the circle circumscribing a triangle is the same as

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