Two chords AB and CD intersect inside a circle at point P. If AP = 4, PB = 9, and CP = 3, what is the length of chord CD?
Answer and explanation
Correct answer: C. 15
- Step 1: By the intersecting chords theorem: AP PB = CP PD.
- Step 2: Substitute values: 4 9 = 3 PD, so 36 = 3 * PD.
- Step 3: PD = 36 / 3 = 12.
- Step 4: Total length of chord CD = CP + PD = 3 + 12 = 15.
Answer
15.
Why not the others: 12 is PD, not the full chord CD; 16 computes 4 * 4; 18 computes 36 / 2.
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