Geometry

Quantitative Aptitude (CGL)

Title

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In a circle, chords PQ and TS are produced to meet at R. If RQ = 14.4 cm, PQ = 11.2 cm, and SR = 12.8 cm, then the length of chord TS is:

This questions was previously asked in

SSC CGL 9th March 2020 Shift-2

16 cm

14.2 cm

- We have chords PQ and TS of a circle, extended to intersect at R.

- Given: RQ = 14.4 cm, PQ = 11.2 cm, SR = 12.8 cm.

- To find TS, apply the chord length property.

- The property states: \((RQ) \times (PR) = (SR) \times (RT)\).

- Calculate PR: \(PR = RQ - PQ = 14.4 - 11.2 = 3.2 \, \text{cm}\).

- Let TR = x, so TS = TR + SR = x + 12.8.

- Using \((RQ) \times (PR) = (SR) \times (RT)\), we get:

\[14.4 \times 3.2 = 12.8 \times x\].

- Solving: \(46.08 = 12.8 \times x \Rightarrow x = \frac{46.08}{12.8} = 3.6 \, \text{cm}\).

- \(\text{So, TS} = 3.6 + 12.8 = 16 \, \text{cm}\).

- The correct option is 1: 16 cm.

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