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Question

# AB and CD are two chords of a circle with centre O such that AB > CD. E and F are the midpoints of AB and CD respectively. Then: Statement 1: OE > OF Statement 2: ∠AOB>∠COD

A
Both statement 1 and statement 2 are true.
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B
Statement 1 is true, while statement 2 is false.
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C
Statement 1 is false, while statement 2 is true.
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D
Both statement 1 and statement 2 are false.
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Solution

## The correct option is C Statement 1 is false, while statement 2 is true.Given that chord AB is longer than chord CD, AB is closer to the centre of the circle than CD is. Since OE and OF are the distances of chords AB and CD respectively from the centre, OE < OF. Also, longer the chord, greater the angle it subtends at the centre. Hence, ∠AOB>∠COD. Thus, statement 1 is false, while statement 2 is true.

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