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What will be the distance between two parallel chords of lengths 30 cm and 16cm drawn on the opposite sides of the center of a circle of radius 17 cm?

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23cm

24cm

25cm

32cm

answer is A.

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Detailed Solution

It is given that two parallel chords of lengths 30 cm and 16cm are drawn on the opposite sides of the center of a circle of radius 17 cm.
Question Image

We know that the perpendicular from the centre of a circle to a chord bisects the chord.

A L = 12 A B = 12 (30) = 15 cm

C M = 12 C D = 12 (16) = 8 cm

For right-angled ∆ALO,
Applying pythagoras theorem,

{AO}^{2} = {OL}^{2} + {AL}^{2}

\Rightarrow {OL}^{2} = {AO}^{2} - {AL}^{2}

= 17^{2} - 15^{2}

= 289 - 225

= 8 cm

For right-angled ∆CMO,
Applying Pythagoras Theorem,

{CO}^{2} = {CM}^{2} + {OM}^{2}

\Rightarrow {OM}^{2} = {CO}^{2} - {CM}^{2}

= 17^{2} - 8^{2}

= 289 - 64

= 15 cm

Adding the value of OM and OL ,
OM+OL=8+15
=23 cm
So, the distance between the chords is 23 cm.
Therefore, option 1 is correct.

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