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Question

An equilateral triangle of side 9 cm is inscribed in a circle. Find the radius of the circle.

A
33 cm
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B
6 cm
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C
32 cm
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D
3 cm
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Solution

The correct option is A 33 cm
Let triangle ABC be an equilateral triangle of side 9 cm, and AD be the median, where G is the centroid of the triangle that divides the median into 2:1.
GD is perpendicular to BC.
In the right-angled triangle ADB,
AD2+DB2=AB2, where AB=9 cm and BD=4.5 cm.
AD2+(92)2=92
AD2=92(92)2
AD2=81(814)
AD=932cm
Radius =23(AD)=23(932)=33cm

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