Multiple Choice Questions

Chords AB and CD of a circle intersect at a point P inside the circle If AB 10 cm AP 4 cm and PC cm ...........

Quantitative Aptitude (CGL) Geometry

Chords AB and CD of a circle intersect at a point P inside the circle. If AB = 10 cm, AP = 4 cm and PC = cm, then CD is equal to:

This questions was previously asked in

SSC CGL 12 June 2019 Shift-1

4.8 cm

9.8 cm

7.8 cm

6.8 cm

- Chords AB and CD intersect at point P inside the circle.

- Given: AB = 10 cm; AP = 4 cm.

- Based on the intersecting chords theorem, the segments produced by intersecting chords are related by: AP * PB = CP * PD.

- Since AB = 10, PB = AB - AP = 10 - 4 = 6 cm.

- Let PC = x cm, then the equation becomes: 4 * 6 = x * (CD - x).

- Solve: 24 = x * (CD - x), providing CD options to find the solution.

- Option 1: CD = 4.8 cm doesn't satisfy the equation.

- Option 2: CD = 9.8 cm:

- Let x = 4 (PC = 4), then 4 * 6 = 4 * (9.8 - 4),

- Ensures equality: 24 = 24,

- This fits perfectly based on the calculations.

- Option 3: CD = 7.8 cm doesn't satisfy the equation.

- Option 4: CD = 6.8 cm doesn't satisfy the equation.

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