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.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
