Mathematics
ABC is an isosceles triangle inscribed in a circle. If AB = AC = cm and BC = 24 cm, find the radius of the circle.
Circles
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Answer
From figure,
OA = radius = r cm.
BD = DC = = 12 cm (As perpendicular to a chord from the center of the circle bisects it)
In right angle triangle ABD,
OD = AD - OA = (24 - r) cm.
In right angle triangle OBD,
⇒ OB = radius = r cm.
⇒ OB2 = OD2 + BD2
⇒ r2 = (24 - r)2 + 122
⇒ r2 = 576 + r2 - 48r + 144
⇒ r2 - r2 + 48r = 720
⇒ 48r = 720
⇒ r = = 15 cm.
Hence, radius = 15 cm.
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