A circle has a radius of 17 cm. Two of its chords are parallel and separated by a distance of 23 cm. If the length of one of these chords is 30 cm, find the length of the second chord.
Show answer & explanation
Correct answer: B
Explanation
Given:
Radius of the circle = 17 cm
First chord = 30 cm
Distance between the two chords = 23 cm
According to the formula:
Distance of the chord from the center = √(r² − (l/2)²)
For the first chord:
l₁ = 30
Distance from the center:
d₁ = √(17² − 15²)
= √(289 − 225)
= √64
= 8 cm
d₁ + d₂ = 23
8 + d₂ = 23
d₂ = 15 cm
Now, the length of the second chord:
l₂ = 2√(17² − 15²)
= 2√(289 − 225)
= 2√64
= 2 × 8
= 16 cm