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
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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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
length of common chord AC is 6cm
hope it helps
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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
length of common chord AC is 6cm
hope it helps
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