Question

. 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.
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Answer 1

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Answer 2

Given :-

Radius of first circle = 5 cm

Radius of second circle = 3 cm

Distance between centres = 4 cm

To Find :-

The length of the common chord.

Solution :-

(Please refer to the attachment provided for better understanding.)

Given that,

OP = 5 cm

OS = 4 cm

PS = 3 cm

PQ = 2PR

Suppose that,

RS = x

Considering ΔPOR,

OP² = OR² + PR²

5² = (4-x)² + PR²

25 = 16+x² - 8x + PR²

∴ PR² = 9-x² + 8x  ----(1)

Considering ΔPRS,

PS² = PR² + RS²

3² = PR² + x²

∴ PR² = 9-x²  ----(2)

By equating (1) and (2),

9 -x² + 8x = 9-x²

8x = 0

x = 0/8

x = 0

Putting the value of x in (1),

PR² = 9-0²

PR = 3 cm

The length of the cord (PQ) = 2PR

Substituting them,

PQ = 2 × 3

PQ = 6 cm

Therefore, the length of the common chord is 6 cm.