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

Answer :

TPS
See the attachment.
O is the centre of larger circle and P is the centre of smaller circle.
We need to find the chord length or 2y.

From ΔACP
x² + y² = 9

From ΔACO
y² + (4+x)² = 5²
⇒ y² + (16 + x² + 8x) = 25
⇒ x² + y² + 8x + 16 = 25
⇒ 9 + 8x + 16 = 25
⇒ 25 + 8x = 25 
⇒ 8x = 25-25 =0
⇒ x = 0

0 + y² = 9
⇒ y = √9 = 3
2y = 2*3 = 6cm

So length of common chord is 6cm. 

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