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Question

In a circle whose radius is 10 inches, a chord is 6 inches from the center. What is the length of the chord?

A
4 inches
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B
6 inches
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C
8 inches
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D
16 inches
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Solution

The correct option is D 16 inches
Let O be the center of the circle and AB be a chord of length.
From O, perpendicular OP is drawn on AB and OA is joined.
Thus, P is the midpoint of AB.
OA=10 inches
OP=6 inches
So, from the right angled ΔOAP,
OA2=AP2+OP2
10262=AP2
10036=AP2
64=AP2
Squaring on both the sides we get,
AP=8 inches
Hence, the length of the chord, AB=8×2=16 inches.
508072_474058_ans_8702017851da4075aec169367c55699c.png

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