Two equal circles pass through each other's centre. If the radius of each of the circle is 13 cm, then what is the length of the common chord?

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Given two equal circles each with radius r = 13 cm, and each passes through the other's center. This means the distance between the centers (d) is equal to the radius, d = 13 cm.

We need to find the length of the common chord.

Step 1: The common chord is the chord of intersection of the two circles.

Step 2: The distance between the centers is d = 13 cm.

Step 3: The length of the common chord (L) can be found using the formula:
L = 2 * sqrt(r^2 - (d^2 / 4))

Step 4: Substitute the values:
L = 2 * sqrt(13^2 - (13^2 / 4))
= 2 * sqrt(169 - (169 / 4))
= 2 * sqrt(169 - 42.25)
= 2 * sqrt(126.75)

Step 5: Simplify sqrt(126.75):
126.75 = 169 * (3/4) = 169 * 0.75
sqrt(126.75) = sqrt(169 * 3/4) = 13 * sqrt(3/4) = 13 * (sqrt(3)/2)

Step 6: So,
L = 2 * 13 * (sqrt(3)/2) = 13 * sqrt(3)

Therefore, the length of the common chord is 13√3 cm.

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