Question

Find the radius of j segment KL has a length of 8 round your answer to the nearest hundredth

Answer 1

x = 5.38

Step-by-step explanation

L and K are points on the circle. The distance from the center of the circle, J, to any point on the circle is the radius, x,

So half the segment KL, the radius x, and the distance from segment KL to the center form two congruent right triangles. The segment from J to segment KL is perpendicular, so it is the bisector of segment KL.

In these right triangles, the radius is the hypotenuse, and the legs are 3.6 units and 4 units long. Using the Pythagorean theorem,

`x=\sqrt[]{3.6^2+4^2}=\sqrt[]{12.96+16}=\sqrt[]{28.96}\approx5.38`

Hence, the radius is 5.38 units, rounded to the nearest hundredth.