Question

Two circle of radius 5cm and 3 cm intersect at two points and the distance between their centre is 4 cm .Find the length of the common chord

Answer 1

Given : In two circles with centres O and O' with radius 5cm and 3cm respectively meet at two points A and B and distance between O and O' is 4cm.

To Find : length of common chord AB

Construction : join the centers of both the circles ans draw prependicular AC from a on OO' of ΔAOO'.

proof ΔAOO' form a right angled triangle as 5,3,4are Pythagorean triplets
5² = 4² + 3²

the line adjoining the common cord makes 90° angle on OO'

area of ΔAOO' = 1/2 × base × height
= 1/2 × 4 × AC
= 2×AC

area of ΔAOO' = 1/2 × 3 × 4
= 6cm²

6 = 2×AC
6/2 = AC
AC = 3cm

AC = AB + BC
= (2×3) cm
= 6 cm

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length of common chord AC is 6cm

hope it helps