Multiple choice

PQ and RS are two parallel chords of a circle whose centre is O and radius is $10$ cm. If PQ $= 16$ cm and RS $= 12$ cm. Then the distance between PQ and RS, if they lie. (i) on the same side of the centre O and (ii) on the opposite of the centre O are respectively

  1. $8$ cm & $14$ cm
  2. $4$ cm & $14$ cm
  3. $2$ cm & $14$ cm
  4. $2$ cm & $28$ cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Distance of chord from center d = sqrt(r^2 - (chord/2)^2). For PQ: d1 = sqrt(100 - 64) = 6. For RS: d2 = sqrt(100 - 36) = 8. Same side: |8 - 6| = 2. Opposite side: 8 + 6 = 14.

AI explanation

Using the property that the perpendicular from the center bisects a chord, the distance from the center to PQ is sqrt(10^2 - 8^2) = 6 cm. The distance from the center to RS is sqrt(10^2 - 6^2) = 8 cm. If they lie on the same side of the center, the distance between them is the difference of these values, which is 8 - 6 = 2 cm. If they lie on opposite sides, the distance is the sum, which is 6 + 8 = 14 cm.

Keep practicing — related questions