Relation between Inradius and Perimeter of Triangle
In a circle w...
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 D16 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 102−62=AP2 100−36=AP2 64=AP2 Squaring on both the sides we get, AP=8 inches Hence, the length of the chord, AB=8×2=16 inches.