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Question
The radius of a circle is 17.0 cm and the length of the perpendicular drawn from its center to a chord is 8.0 cm.
Calculate the length of the chord.
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.
∴ AC = CB
In ΔOCA,
OA2 = OC2 + AC2 ...( By Pythagoras theorem )
⇒ AC2 = (17)2 - (8)2 = 225
⇒ Ac = 15 cm
∴ AB = 2 AC = 2 x 15 = 30 cm.
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