Multiple choice

In a circle of radius $13$cm, $PQ$ and $RS$ are two parallel chords of length $24$cm and l0cm respectively. The chords are on the opposite sides of the centre. The distance between the chords is?

  1. $7$cm
  2. $17$cm
  3. $26$cm
  4. $12$cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The distance from the centre to a chord is sqrt(r^2 - (chord/2)^2). For the 24 cm chord this is 5 cm, and for the 10 cm chord it is 12 cm. Since the chords lie on opposite sides, their separation is 5 + 12 = 17 cm.

AI explanation

For the first chord PQ of length 24 cm, half the chord is 12 cm, and using the Pythagorean theorem with the radius of 13 cm, the distance from the center is sqrt(13^2 - 12^2) = sqrt(169 - 144) = 5 cm. For the second chord RS of length 10 cm, half the chord is 5 cm, making its distance from the center sqrt(13^2 - 5^2) = sqrt(169 - 25) = 12 cm. Since the chords are on opposite sides of the center, the total distance between them is the sum of their individual distances from the center, which is 5 + 12 = 17 cm.

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