Question

Two circles touch each other externally. The sum of their areas is 1540 sq.cm. Their centres are separated by 28 cm. Then the difference of their radii (in m) is ________

a) 14

b) 7

c) 0.07

d) 0.14​

Answer 1

Step-by-step explanation:

let R1 and R2 be the radius of first and second circle respectively ,

hence

area of first circle = πR1²

similarly for second circle = πR2²

but ,

πR1² + πR2² = 1540, sum of areas of circle

R1² + R2² = 1540/ 3.14 = 490.44

and , R1 + R2 = 28

R2 = 28- R1

put this value we get

R1² + (28 -R1)² = 490.44

R1² + 28² + R1² - 2× 28 × R1 = 490.44

2R1² -56R1 +293.56 = 0

R1² -28R1 + 146.78 = 0

R1 = 28(+-) √(28² -4× 1×146.78) /2

R1 = 14(+-) 7

R1 = 7 , 21

so , that

R2 = 28-R1 = 21, 14

difference of radius = |R1-R2| = 14cm or 7 cm

= 0.14m or 0.07m

option c and d is correct.