What is the distance ( in cm) between two parallel cords of length 32 cm and…
2025
What is the distance ( in cm) between two parallel cords of length 32 cm and 24 cm in a circle of radius 20 cm ?
- A.
4 or 28
- B.
2 or 14
- C.
1 or 7
- D.
3 or 21
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Show answer & explanation
Correct answer: A
Solution:
Let the perpendicular distances from the center to the chords be x and y.
For the 32 cm chord: half-length = 16 cm. Using the right triangle formed by the radius, half-chord and perpendicular distance, x^2 + 16^2 = 20^2 ⇒ x^2 = 400 − 256 = 144 ⇒ x = 12 cm.
For the 24 cm chord: half-length = 12 cm. Similarly, y^2 + 12^2 = 20^2 ⇒ y^2 = 400 − 144 = 256 ⇒ y = 16 cm.
Because the chords are parallel they may lie on the same side of the center or on opposite sides. If on the same side, distance between chords = |16 − 12| = 4 cm. If on opposite sides, distance = 16 + 12 = 28 cm.
Answer: 4 cm or 28 cm.