An equilateral triangle of side 6 cm is inscribed in a circle. Find the radius of the circle.
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Question

An equilateral triangle of side 6 cm is inscribed in a circle. Find the radius of the circle.

KnowledgeBoat · Accepted 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.

Mathematics

An equilateral triangle of side 6 cm is inscribed in a circle. Find the radius of the circle.

Circles

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