Multiple choice

Chord AB and CD of a circle intersect externally at P. If AB = 6 cm, CD = 3 cm and PD = 5 cm, then the length of PB is -

  1. 5 cm

  2. 6.25 cm

  3. 6 cm

  4. 4 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For intersecting chords, PA × PB = PC × PD. Given CD = 3 cm and PD = 5 cm, then PC = CD - PD = -2 cm, which is impossible as lengths are positive. This suggests P lies outside the circle (external intersection). For external intersection: PA × PB = PC × PD. Let PB = x. Since P is external, PA = PB + AB = x + 6. Also PC = PD + CD = 5 + 3 = 8. So (x+6)x = 8×5 = 48. x² + 6x - 48 = 0. Solving: x = 6 cm.

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