Two circles of radii 5 cm and 3 cm intersect at two points and the distance betweentheir centres is 4 cm. Find the length of the common chord
Question
Two circles of radii 5 cm and 3 cm intersect at two points and the distance betweentheir centres is 4 cm. Find the length of the common chord
Solution
To find the length of the common chord, we can use the formula for the length of the chord of a circle, which is given by:
Length of chord = 2 * sqrt[r1*r2 - (d^2)/4]
where: r1 and r2 are the radii of the two circles (5 cm and 3 cm respectively), d is the distance between the centres of the two circles (4 cm).
Substituting the given values into the formula, we get:
Length of chord = 2 * sqrt[(5*3) - (4^2)/4] = 2 * sqrt[15 - 4] = 2 * sqrt[11] = 2 * 3.31662479 = 6.63324958 cm
So, the length of the common chord is approximately 6.63 cm.
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