Question : Chords 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:
Option 1: 5 cm
Option 2: 7.35 cm
Option 3: 6 cm
Option 4: 4 cm
Correct Answer: 7.35 cm
Solution : Given: AB = 6 cm, CD = 3 cm PD = 5 cm, PB = ? We know that, PA × PB = PC × PD ⇒ (PB – 6) PB = 2 × 5 ⇒ PB 2 – 6PB – 10 = 0 ⇒ PB = $\frac{6\pm\sqrt{36+40}}{2}$ ⇒ PB = $\frac{6\pm\sqrt{76}}{2}$ $\therefore$ PB = $\frac{6+8.7}{2}$ = 7.35 Hence, the correct answer is 7.35 cm.
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