Mathematics

Problem

A circle has radius

9\,\text{cm}

. Two chords

AB

and

CD

are at perpendicular distances of

3\,\text{cm}

and

6\,\text{cm}

respectively from the centre. (i) Without performing any calculation, state which chord is longer and give a reason based on a property of chords. (ii) If a third chord

EF

is longer than

CD

but shorter than the diameter, what can you say about the distance of

EF

from the centre? Explain briefly.

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