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Question
In the given figure, O is the center 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) the radius of the circle
(ii) length of chord CD.
Solution
(i) AB is the chord of the circle and OM is perpendicular to AB.
So, AM = MB = 12 cm ....( Since ⊥ bisects the chord )
In right ΔOMA,
OA2 = OM2 + AM2
⇒ OA2 = 52 + 122
⇒ OA = 13 cm
So, radius of the circle is 13 cm.
(ii) So, OA = OC = 13 cm ....( radii of the same circle )
In right ΔONC,
NC2 = OC2 - ON2
⇒ NC2 = 132 - 122
⇒ NC = 5 cm
So, CD = 2NC = 10 cm.
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