Multiple Choice Questions

From an external point A two tangents AB and AC have been drawnto a circle touching the circle at B ...........

Quantitative Aptitude (CGL) Geometry

From an external point A, two tangents AB and AC have been drawnto a circle touching the circle at B and C respectively. P and

Q are points on AB and AC respectively such that PQ touchesthe circle at R. IfAB = 11 cm, AP=7 cm and AQ = 9 cm, then find

the length of PQ (in cm).

This questions was previously asked in

SSC CGL 16th August 2021 Shift-2

- In the given scenario, AB and AC are tangents drawn from point A to the circle, touching the circle at points B and C respectively.

- The lengths provided are: AB = 11 cm, AP = 7 cm, and AQ = 9 cm.

- Because AB and AC are tangents from the same external point A, AB = AC.

- Therefore, AC also measures 11 cm.

- The segment PQ touches the circle at point R, making it a tangent as well.

- Since AP = 7 cm, BP measures 4 cm (because AB = AP + PB = 7 + 4 = 11).

- Since AQ = 9 cm, CQ equals 2 cm (because AC = AQ + QC = 9 + 2 = 11).

- By the property of tangents drawn from an external point, BP = CQ.

- Therefore, PQ = 4 + 2 = 6 cm.

Correct Answer: Option 4 - 6 cm.

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