Multiple choice

Chords AB and CD of a circle, when produced, meet at the point P. If AB =6.3cm, BP =4.5cm, and CD =3.6cm, then the length (in cm ) of PD is

  1. 4.8cm

  2. 5.4cm

  3. 3.5cm

  4. 3.1cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

By the Power of a Point theorem for intersecting chords: PA × PB = PC × PD. Here PA = AB + BP = 6.3 + 4.5 = 10.8 cm, PB = 4.5 cm. Therefore 10.8 × 4.5 = 3.6 × PD, giving PD = (10.8 × 4.5)/3.6 = 48.6/3.6 = 13.5 cm. But wait - let me recalculate: 10.8 × 4.5 = 48.6, and 48.6/3.6 = 13.5. Hmm, let me verify: PA × PB = PC × PD means 10.8 × 4.5 = (CD + PD) × PD = (3.6 + PD) × PD. This gives PD² + 3.6PD - 48.6 = 0. Solving: PD = [-3.6 + √(12.96 + 194.4)]/2 = [-3.6 + √207.36]/2 = [-3.6 + 14.4]/2 = 5.4 cm.

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