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Question

AB and CD are equal chords. If OE is 3 cm and AB is 8 cm, then the value of OC is .

A
4 cm
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B
6 cm
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C
5 cm
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D
3 cm
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Solution

The correct option is C 5 cm
In the given figure,Given: AB = CD = 8 cm and OE = 3 cm.
We know that, a line drawn through the centre bisects the chord and is perpendicular to it.
Thus, CF=CD2=4cm
OE = OF = 3 cm ..... (Equal chords of a circle are equidistant from the centre.)
Consider ΔOFC,
OF2+CF2=OC2 .....(Pyhtagoras Theorem)
32+42=OC2
OC2=9+16=25
Thus, OC = 5 cm.

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