Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.

To solve this problem, we can use the formula for the length of a common chord between two intersecting circles. The formula is:

Length of common chord = 2 * sqrt[(r1^2 - d^2) + (r2^2 - d^2)]

where r1 and r2 are the radii of the two circles and d is the distance between their centres.

Step 1: Substitute the given values into the formula.

Length of common chord = 2 * sqrt[(5^2 - 4^2) + (3^2 - 4^2)]

Step 2: Simplify the equation.

Length of common chord = 2 * sqrt[(25 - 16) + (9 - 16)]

Step 3: Continue simplifying.

Length of common chord = 2 * sqrt[9 + (-7)]

Step 4: Simplify further.

Length of common chord = 2 * sqrt[2]

Step 5: Calculate the square root of 2 (approximately 1.41).

Length of common chord = 2 * 1.41

Step 6: Multiply to find the final answer.

Length of common chord = 2.82 cm

So, the length of the common chord is approximately 2.82 cm.