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

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, ⇒ AB 2 = AD 2 + BD 2 ⇒ 6 2 = AD 2 + 3 2 ⇒ AD 2 = 36 - 9 ⇒ AD 2 = 27 ⇒ AD = = cm. OD = AD - AO = cm. In right angle triangle OBD, ⇒ OB = radius = r cm. ⇒ OB 2 = OD 2 + BD 2 ⇒ r 2 = 2 + 3 2 ⇒ r 2 = 27 + r 2 - r + 9 ⇒ r 2 - r 2 + r = 36 ⇒ r = 36 ⇒ r = cm. Hence, radius = cm.

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A rectangle with one side of length 4 cm is inscribed in a circle of diameter 5 cm. Find the area of rectangle.

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AB and CD are two parallel chords of a circle of lengths 10 cm and 4 cm respectively. If the chords lie on the same side of the centre and the distance between them is 3 cm, find the diameter of the circle.

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AB is a diameter of a circle. M is a point in AB such that AM = 18 cm and MB = 8 cm. Find the length of the shortest chord through M.

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Mathematics

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

Circles

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AB and CD are two parallel chords of a circle of lengths 10 cm and 4 cm respectively. If the chords lie on the same side of the centre and the distance between them is 3 cm, find the diameter of the circle.

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