In a circle of radius 10 cm, two parallel chords of lengths 12 cm and 16 cm lie on opposite sides of the centre. Determine the distance separating these two chords.
Show answer & explanation
Correct answer: A
Explanation
Given:
Radius of the circle = 10 cm
Two parallel chords = 12 cm and 16 cm
Both chords are in opposite directions from the center
By the formula:
Distance of the chord from the center = √(r² − (l/2)²)
For a 16 cm chord
Distance = √(10² − 8²)
= √(100 − 64)
= √36
= 6 cm
For a 12 cm chord
Distance = √(10² − 6²)
= √(100 − 36)
= √64
= 8 cm
Both chords are in opposite directions
Hence, the total distance = 6 + 8 = 14 cm
Distance between the two chords = 14 cm