ABC is an isosceles triangle inscribed in a circle. If AB = AC = cm and BC = 24 cm, find the radius of the circle.

Question

KnowledgeBoat · Accepted 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.

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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