In a circle with center O, two parallel chords AB and CD are on opposite sides of the center. If the length of chord AB is 16 cm and chord CD is 12 cm, and the distance between them is 14 cm, find the radius of the circle.
Show answer & explanation
Correct answer: B
Explanation
Given:
Chord AB = 16 cm
Chord CD = 12 cm
Distance between the two chords = 14 cm
By the formula:
r² = d² + (c/2)²
Let the distance of AB from the center = x
For AB
r² = x² + (16/2)²
r² = x² + 8²
r² = x² + 64
For CD
r² = (14 − x)² + (12/2)²
r² = (14 − x)² + 6²
r² = (14 − x)² + 36
x² + 64 = (14 − x)² + 36
x² + 64 = 196 − 28x + x² + 36
64 = 232 − 28x
28x = 168
x = 6
r² = 6² + 64
r² = 36 + 64
r² = 100
r = 10
Radius of the circle = 10 cm