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

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

KnowledgeBoat · Accepted Answer

Let ABC be equilateral triangle inscribed in circle. AB = BC = AC Draw AD BC. Since, in an equilateral triangle the perpendicular from a vertex bisects the opposite side. Thus, D is the mid-point of BC. BD = = 4.5 cm. Since, the chord BC is bisected at point D, and perpendicular from center bisects the chord. Centre of the circle O lies on AD. Let radius of circle (OA) be r. In right-angled triangle ADB, By pythagoras theorem, ⇒ Hypotenuse2 = Perpendicular2 + Base2 ⇒ AB2 = AD2 + BD2 We know that, In an equilateral triangle, the centroid and circumcentre coincide. Since AD is a median, and centroid divides median in 2:1 ratio, AO : OD = 2 : 1 Radius (AO) = = cm. Hence, the radius of the circle = cm.

Mathematics

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

Circles

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