Two parallel chords of a circle, with lengths 16 cm and 12 cm, are on opposite sides of the center. If the distance between the two chords is 14 cm, what is the radius of the circle?
Show answer & explanation
Correct answer: A
Explanation
Given:
Chords = 16 cm and 12 cm
Both chords are on opposite sides of the center
Distance between the two chords = 14 cm
Formula:
Distance of chord from the center = √(r² − (l/2)²)
Let
Distance of the 16 cm chord from the center = x
Distance of the 12 cm chord from the center = y
Since the chords are on opposite sides,
x + y = 14
x = √(r² − 8²)
y = √(r² − 6²)
√(r² − 64) + √(r² − 36) = 14
If r = 10
√(100 − 64) + √(100 − 36)
= √36 + √64
= 6 + 8
= 14
Radius = 10 cm