Question

plz someone tell the ans of 1 ques

Answer 1

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

OP = 5 cm, OâP = 3 cm, OOâ = 4 cm.

Let OL = x, so LOâ = 4 - x

Let PQ = y, so PL = y/2

In right triangle OLP,

OL2 = (OP2 â LP2) = 52 â (y/2)2

=> x2 = 25 â y2/4 â¦(i)

In right triangle OâLP, OâL2 = (32 â y2/4)

(4 â x)2 = 9 â y2/4 â¦(ii)

From (i) and (ii) we get

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

=> 8x =32

=> x = 4

From equation (i)

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

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