Question

the circumference of circle C1 is 66 cm. this circle touches all the chords of length 56 cm of circle C2. what is the difference between areas of the two circles?​

Answer 1

Answer:

Let, (Ra) and (Rb) be radii of circle A and circle B respectively.

From, the plot of this problem, it is clear that both the circles are concentric.

Now, 2 * (22 / 7) * (Ra) = 66 cm

(Ra) = (21 / 2) cm = 10.5 cm

Now, we know that, perpendicular drawn from centre on any chord bisects it.

So, (Rb)^2 = {(Ra)^2} + {(touching chord / 2)^2}

= (10.5)^2 + {(56 / 2)^2}

(Rb)^2 = (110.25 + 784) cm^2 = 894.25 cm^2

Difference of areas between the two circles = (22 / 7) * [{(Rb)^2} - {(Ra)^2}] = (22 / 7) * 784 cm^2 = 2464 sq cm.