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Question
In the figure given below, O is the centre of the circle. AB and CD are two chords of the circle. OM is perpendicular to AB and ON is perpendicular to CD.
AB = 24 cm, OM = 5 cm, ON = 12 cm. Find the
(i) radius of the circle
(ii) length of chord CD.
Solution
AB = 24 cm, OM = 5 cm, ON = 12 cm.
(i) In Δ AOM,
OA2 = OM2 + AM2
OA2 = 52 + 122
OA2 = 25 + 144 = 169
OA = 13 cm.
Thus, radius of the circle is 13 cm.
(ii) In Δ CON,
OC2 = ON2 + CN2
132 = 122 + CN2 ....( ∵ OC = OA = 13 (Radius))
169 - 144 = CN2
CN2 = 25
CN = 5.
Thus length of chord CD = 2CN = 2 x 5 = 10 cm
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