Question

Suppose a chord of a circle is 16cm and is 12 cm from the center of the circle. find the radius.

Answer 1

The radius of the circle is approximately 14.42cm

Explanation:

If the length of the chord is 16cm and it is 12cm from the center of the circle.

it means it forms 2 right angles while dividing the center of the chord, to the center of the circle, and at right angle. Length of the adjacent then become 16/2 = 8cm

To calculate the radius which forms hypothenus of the right angle triangle, we use Pytagoras Theorem

Say
`r^(2)` =
`12^(2)` +
`8^(2)` , where r is the radius of the circle

`r^(2)` = 144 + 64

`r^(2)` = 208

r =
`√(208)`

r = 14.4222

r ≈ 14.42