The radius of a circle is 2.5 cm. AB and CD are two parallel chords 2.7 cm apart. If the length of the chord AB is 4.8 cm, then find the length of chord CD.

4.8 cm

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2.4 cm

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3 cm

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4 cm

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Solution

The correct option is C
3 cm

Since the perpendicular from the centre of the circle bisects the chord, AP = 2.4 cm

Using Pythagoras theorem for $Δ A P O$ , we can calculate $P O = \sqrt{{2.5}^{2} - {2.4}^{2}} = 0.7 c m$

Since PQ = 2.7 cm and PO = 0.7 cm, OQ = 2 cm

Using Pythagoras theorem for $Δ C Q O, C Q = \sqrt{{2.5}^{2} - 2^{2}} = 1.5 c m$

So, CD = 2CQ = 3 cm

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