Question

Part A In the figure shown below, O is the center of the circle. Find the value of x. Part B For the figure shown above, what is the length of AB ?​

Answer 1

Part A : x = 26

Part B : AB = 64

Explanation:

Part A,

By the theorem,

"Perpendicular drawn from the center of a circle to the chord is a bisector of the chord."

Since ON is a perpendicular to the chord AB,

AN = BN

x + 6 = 2x - 20

x = 2x - 20 - 6

x = 2x - 26

x - 2x = -26

-x = -26

x = 26

Part B,

Length of AB = (x + 6) + (2x - 20)

= 3x - 14

For x = 26

AB = (3×26 - 14)

= 78 - 14

= 64

Therefore, Option (D) will be the answer.