Question

PLEASE HELP!!! Find the length of the radius. Write your answer as a simplified radical.

Answer 1

Step-by-step explanation:

Hey there!

Here;

A chord of a circle AB is given with measure of 24 cm.

Let O be the centre of a circle and OP is perpendicular to AB.

Now, draw an imaginary line from O to B. [To make a radius].

Now;

$bp = \frac{1}{2} \times ab$

$bp = \frac{1}{2 } \times 24$

Therefore BP = 12.

Again;

You can clearly see that POB is a Right angled triangle.

Now,

Using Pythagoras relation we get;

${ob} = \sqrt{ {po}^{2} + {bp}^{2} }$

$ob = \sqrt{ {8}^{2} + {12}^{2} }$

$ob = \sqrt{64 + 144}$

$ob = \sqrt{208}$

Therefore OB = 14.42.

As OB is a radius, the value of radius is 14.42.

Hope it helps...