Mathematics
An equilateral triangle of side 6 cm is inscribed in a circle. Find the radius of the circle.
Circles
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Answer
From figure,
OA = radius = r cm.
BD = DC = = 3 cm (As perpendicular to a chord from the center of the circle bisects it)
In right angle triangle ABD,
⇒ AB2 = AD2 + BD2
⇒ 62 = AD2 + 32
⇒ AD2 = 36 - 9
⇒ AD2 = 27
⇒ AD = = cm.
OD = AD - AO = cm.
In right angle triangle OBD,
⇒ OB = radius = r cm.
⇒ OB2 = OD2 + BD2
⇒ r2 = 2 + 32
⇒ r2 = 27 + r2 - r + 9
⇒ r2 - r2 + r = 36
⇒ r = 36
⇒ r = cm.
Hence, radius = cm.
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