Exams › SSC CGL (Prelims) › General

Two parallel chords of lengths 20 cm and 14 cm lie on the same side of the centre of a circle. The distance between them is 3 cm. What is the radius of the circle?

1. $\sqrt{143}$ cm
2. $\sqrt{140}$ cm
3. $\sqrt{149}$ cm
4. $\sqrt{134}$ cm

Correct answer: $\sqrt{149}$ cm

Solution

If the distances of the 20 cm and 14 cm chords from the centre are $x$ and $x+3$, then $20=2\sqrt{r^2-x^2}$ and $14=2\sqrt{r^2-(x+3)^2}$. Solving these gives $x=6$ and $r^2=149$. Therefore, the radius is $\sqrt{149}$ cm.

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