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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.

Posted by Sumedha Kamble 4 years ago

Gaurav Seth 4 years ago

Let O and O’ be the centres of the circles of radii 5 cm and 3 cm respectively and let PQ be their common chord.

OP = 5 cm, O’P = 3 cm, OO’ = 4 cm.

Let OL = x, so LO’ = 4 - x

Let PQ = y, so PL = y/2

In right triangle OLP,

OL² = (OP² – LP²) = 5² – (y/2)²

=> x² = 25 – y²/4 …(i)

In right triangle O’LP, O’L² = (3² – y²/4)

(4 – x)² = 9 – y²/4 …(ii)

From (i) and (ii) we get

x² – 16 + 8x – x² = 25 – y²/4 – 9 + y²/4

=> 8x =32

=> x = 4

From equation (i)

16 = 25 – y²/4 => y²/4 = 9 => y² = 36 => y = 6

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

ANSWER

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