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Question
A chord of length 8 cm is drawn at a distance of 3 cm from the center of the circle.
Calculate the radius of the circle.
Solution
Let AB be the chord and O be the center of the circle.
Let OC be the perpendicular drawn from O to AB.
We know, that the perpendicular to a chord, from the center of a circle, bisects the chord.
∴ AB = 8 cm
⇒ AC = CB = `"AB"/2`
⇒ AC = CB = `8/2`
⇒ AC = CB = 4 cm
In OCA,
OA2 = OC2 + AC2 ...( By Pythagoras theorem )
⇒ OA2 = ( 4 )2 + ( 3 )2 = 25
⇒ OA = 5 cm
Hence, radius oof the circle is 5 cm.
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