Two circles of equal radius of 2 3 intersect each other in such a way that both pass through center of each other. The length of common chord is (1) 8 (2) 6 (3) 4 (4) 3

The two circles intersect each other in such a way that both pass through the center of each other. This means that the centers of the two circles, and the two points where the circles intersect, form a square.

The diagonal of this square is the diameter of each circle. Given that the radius of each circle is 2√3, the diameter is 2 * 2√3 = 4√3.

In a square, the length of the diagonal (d) can be found from the side length (s) using the formula d = s√2. We can rearrange this formula to find the side length when we know the diagonal: s = d / √2.

Substituting the known diagonal length, the side length of the square is s = 4√3 / √2 = 4√2.

The common chord of the two circles is the side length of the square, so the length of the common chord is 4√2.

This is not one of the options given in the question, so there may be a mistake in the question or the answer choices.

The two circles intersect each other in such a way that both pass through the center of each other. This means that the centers of the two circles, and the two points where the circles intersect, form a square.

The diagonal of this square is the diameter of each circle. Given that the radius of each circle is 2√3, the diameter is 2 * 2√3 = 4√3.

In a square, the length of the diagonal (d) can be found from the side length (s) using the formula d = s√2. We can rearrange this formula to find the side length when we know the diagonal: s = d / √2.

Substituting the known diagonal length, the side length of the square is s = 4√3 / √2 = 4√2.

The common chord of the two circles is the side length of the square, so the length of the common chord is 4√2.

This is not one of the options given, so there may be a mistake in the question or the answer choices.