Multiple choice

Chords $AB$ and $CD$ of circle intersect at $P$. If $AP = 12\ cm, PB = 6\ cm$ and $CP = 2\ cm$, the length of $PD$, in cm, is

  1. $12$
  2. $24$
  3. $36$
  4. $48$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For intersecting chords AB and CD at P, AP * PB = CP * PD. 12 * 6 = 2 * PD. 72 = 2 * PD, so PD = 36.

AI explanation

By the intersecting chords theorem, the product of the segments of one chord equals the product of the segments of the other chord, giving AP times PB equals CP times PD. Substituting the given values results in 12 times 6 equals 2 times PD. Solving this equation, 72 equals 2 times PD, so PD is 36 cm.

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