Question

If a length of a chord of a circle is 16 cm and is at a distance of 15 cm from the centre of a circle then find the radius of a circle

Answer 1

Answer:

AB is the given chord of 16cm length and OM is the perpendicular distance from the center to AB.

We know that perpendicular from the center to any chord divides it into two equal part.

So,AM=MB=16÷2=18cm

Now consider right triangle OMA and by using pythagoras theoram.

AO^2=AM^2+OM^2

=8^2+15^2

=64+225

AO^2=289

AO=√289

=17cm

Answer 2

Given:

Length of the chord=16cm

Distance of the chord from the centre=15cm

To find:

The radius of the circle

Solution:

We can find the radius by following the given process-

We know that a perpendicular drawn from the center of a circle to a chord divides it into two parts equally.

So, the radius, distance of chord from center, and the chord form a right-angled triangle.

Let the radius be R cm.

Using the Pythagoras theorem,

${R}^{2} = {base}^{2} + {perpendicular}^{2}$

Base= Length of chord/2

=16/2=8cm

Perpendicular distance= 15cm

${R}^{2} = {8}^{2} + {15}^{2}$

${R}^{2} = 64 + 225$

${R}^{2} = 289$

R=√289

R= 17 cm

Therefore, the radius of the circle is 17 cm.