Question

two circles of radii 5cm and 3cm intersect at two points and the distance between their centres is 4cm. Find the length of the common chord.
Explain and elaborate no direct answers pls.......

Answer 1

Answer:

Hi mate her is your answer

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 2

hope it's helpful for u........