Question

Find the value of X. If necessary, round your answer to the nearest tenth.

Answer 1

D. 10

Explanation:

The chord is bisected as shown by the perpendicular lines and right angle, so both segments are 6.

Draw a radius from the center to the end of the chord to create a right triangle. 8 and 6 are the legs, use pythagorean theorem to find the length of the segment you drew because its the hypotenuse.

8^2+6^2=x^2

64+36

100

square root of 100 is 10

So, 10 is the length of the segment. Both the x segment and the 10 segment are radii because they are draw from the center to a point on the circle.

They are equal.

x=10

Answer 2

10

EXPLANATION

The value of x is the radius of the circle.

The radius of the circle is also the hypotenuse of the right triangle formed by the chord, the radius and the segment bisecting the chord through the center.

We apply the Pythagoras Theorem to obtain:

`{x}^(2) = {8}^(2) + {6}^(2)`

`{x}^(2) = 64 + 36`

`{x}^(2) = 100`

Take positive square root

`x = √(100)`

`x = 10`