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Perpendicular from the Center to a Chord Bisects the Chord

A chord P Q o...

Question

A chord PQ of length 12 cm subtends an angle of 120° at the centre of a circle. Find the area of the minor segment cut off by the chord PQ.

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Solution

We know that the area of minor segment of angle θ in a circle of radius r is,

It is given that the chord PQ divides the circle in two segments.

We have and. So,

Since,

In, we have

Thus the radius of circle is .

Now using the value of radius r and angle θ we will find the area of minor segment

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Perpendicular from the Center to a Chord Bisects the Chord

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