Chords AB and CD of a circle intersect externally at P If AB 6 cm CD 3 cm and PD 5 cm then the lengt...........

Quantitative Aptitude ( CCS) Geometry

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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

5 cm

7.35 cm

6 cm

4 cm

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Explanation:

Given, PD = 5 cm
Then, PC = PD – CD = 5 – 3 = 2 cm
Similarly, PA = (PB – 6) cm
Note : If two chords AB and CD of a circle intersect inside or outside the circle when produced at a point P, then
PA × PB = PC × PD
⇒ (PB – 6) × PB = 2 × 5
⇒ PB² – 6PB – 10 = 0
By Sridharacharya formula,