Question

chord of length 24 cm is at a distance of 9 cm from the centre of the circle what is the length of the longest chord of the circle​

Answer 1

Concept:-

Here, We have given the length of chord and the distance from the centre to the chord. We have to find here the longest chord of the circle. To finding this we use Pythagoras theorem.

Given:-

• Length of chord is of 24 cm.
• Distance from the centre of the circle to the chord is 9 cm.

To Find:-

• The length of the longest chord of the circle.

Solution:-

Here, Let the radius of the circle be r cm.

We know that,

The perpendicular to a chord, drawn from the centre of the circle, bisects the chord.

So,  AP = BP = 12 cm

Now, By Pythagoras theorem we have,

$\sf{\implies OA^{2} = OP^{2} + AP^{2}}$

$\sf{\implies r^{2} = 9^{2} + 12^{2}}$

$\sf{\implies r^{2} = 81 + 144}$

$\sf{\implies r^{2} = 225}$

$\sf{\implies r = \sqrt{225}}$

$\sf{\implies r = 15\ cm}$

Since, We know that the longest chord of any circle is its diameter.

And, Diameter = 2 × Radius

                        = 2 × 15 cm

                        = 30 cm

Hence, Length of the longest chord of the circle is 30 cm.

Answer 2

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