Question

a chord of length 10cm is at a distance of 12 cm from the centre of the circle .another chord of the same circle is length 24cm .find the distance from the centre​

Answer 1

The distance of chord having length 24 cm from the center is 5 cm.

Step-by-step explanation:

First we draw the figure as shown (attached):

• AB is the chord having length 24 cm and MN is the chord having length 10 cm.

• We are given the distance of chord MN from center O is 12 cm. So, OP = 12 cm

We can understand that $\Delta OPN$ is a right angle triangle:

So, we can apply the Pythagorean theorem:

$ON^2 = OP^2 + PN^2$

 = $12^2 + 5^2$

= $13^2$

ON = 13 cm (This is the radius.)

Now, we observe right angle triangle $\Delta OCA.$

Again apply the Pythagorean theorem.

• $OA^2 = OC^2 + AC^2$

$13^2 = OC^2 + 12^2$

$169 - 144 = OC^2$

OC = 5 cm

This is the required distance.

Thus, the distance of chord having length 24 cm from the center is 5 cm.

Answer 2

Answer:

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