### Question 24

SSC-CGL 2020 Mar 3 Shift 2

A chord is drawn inside a circle of radius 5 cm. What is the length of the chord if its distance from the center of the circle is 3 cm?

### Solution in Detail

PQ is the chord.

distance from center CX = 3 cm

CXP is a right triangle

By pythagoras, PX = 4 cm

But CX is a perpendicular from the center to the chord PQ. By the properties of a circle, it bisects PQ.

$\displaystyle \therefore PQ = 2 \times PX $

$\displaystyle = 2 \times 4 = 8 \text{ cm } \underline {Ans}$

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