PQ and RS are chords on a circle centred at O Suppose A is the point of intersection of PQ and RS Wh...........

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PQ and RS are chords on a circle centred at O. Suppose A is the point of intersection of PQ and RS. Which of the following statements is/are correct?

If A and O coincide, then the four parts of the circle produced by the chords shall always have equal areas.
If A and O do not coincide, then two of the four parts of the circle produced by the chords shall always have equal areas.

Select the correct answer using the code given below

This questions was previously asked in

EPFO APFC 2023

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1 Only

2 Only

Both 1 and 2

Neither 1 nor 2

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Explanation:

Let’s break down the statements:

- Statement 1: If A (intersection of chords) and O (centre) coincide, the chords pass through the centre and are diameters. The two diameters divide the circle into four equal sectors, making the four parts have equal areas. This is true.

- Statement 2: If A and O do not coincide, the chords do not pass through the centre. The parts formed may not be symmetrical, but *two of the four areas will always be equal* because each chord divides the circle into two regions of equal area if and only if it passes through the centre. Otherwise, only the opposite segments created by two intersecting chords are equal. This statement is also true.

Options:

- 1 Only

- 2 Only

- Both 1 and 2 (Correct)

- Neither 1 nor 2

Correct Answer: Option 3 - Both 1 and 2 are correct.