Chords AB and CD of a circle intersect externally at P If AB 7 cm CD I cm and PD 5 cm then the lengt...........

Quantitative Aptitude (CGL) Geometry

Chords AB and CD of a circle intersect externally at P. If AB= 7 cm. CD= I cm and PD= 5 cm, then the length of PB (in cm) is:

This questions was previously asked in

SSC CGL 13th April 2022 Shift-2

Let's solve the problem step by step:

- Chords AB and CD intersect externally at point P.

- AB = 7 cm, CD = 11 cm (assuming "I" is 11), and PD = 5 cm.

- By Power of Point theorem: PA × PB = PC × PD.

- Let PB = x, so PA = 7 – x.

- Let PC = (since PD = 5 and CD = 11, so PC = 11 – 5 = 6).

- Substituting values: (7 – x) × x = 6 × 5.

- (7 – x)x = 30 ? x² – 7x + 30 = 0.

- This quadratic has no real and positive solution (discriminant: 49 – 120 < 0), so none of the answer options work naturally.

- Reviewing options:

- Option 1: 5

- Option 2: 10

- Option 3: 3

- Option 4: 8

- But from above, none fit mathematically given provided data.

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