Question

# Which is the smallest of all the chords of a circle passing through a given point in it?

A
Chord trisected at the point.
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B
Chord bisected at the point.
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C
Chord passing through the centre.
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D
Both (A)and (B)
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Solution

## The correct option is B Chord bisected at the point.Let C (O,r) is a circle and let M is a point within it where O is the centre and r is the radius of the circle. Let CD is another chord passes through point M.We have to prove that AB<CD.Now join OM and draw OL perpendicular to CD.In right angle triangle OLM,OM is the hypotenuse.So OM>OL⇒ chord CD is nearer to O in comparison to AB.⇒ CD>AB⇒ AB<CD⇒ Smallest one is the one bisected at the point.

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