Question

Find the area of a circle circumscribing an equilateral triangle of side 15 cm.

Answer 1

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Answer 2

For these kind of problems always connect the centre with any two vertices .

we have this theorem that the angle subtended at the centre by a chord is double the angle subtended by it on the corresponding segment

so by that we get

angle BOC = 120 =2*60degree

Bo= AC=radius

so we get an isosceles triangle BOC so 120 + angle obc + angle oCB is equal to 180

angle abc=angle ACB

therefore 120 degree + 2 angleObc) =180degrees

this means that OBC = 30

now by constructing a perpendicular from we get angle bop =60 degree by angle sum property