Question

two circle touch is internally the sum of their areas is 130πcm² square and the distance between their centres is 8 cm .find the radius of the two circles.

Answer 1

Let a circle with center O And radius R.
let
another circle inside the first circle  with center o' and radius r .
A/Q,
Area of 1st circle + area of 2nd circle = 116π cm²
⇒ πR² + πr² = 116π 
⇒ π(R² + r²)  = 116π
⇒ R² + r² =116 --------------------(i)
Now,
Distance between the centers of circles = 6 cm
i.e, R - r = 6
⇒  R = r + 6  -------------------(ii)
From Eqn (i) & (ii),
(r + 6)² + r² = 116
⇒ r² + 12r +36 + r² =116
⇒ 2r² +12r +36 -116 = 0
⇒ 2r² +12r - 80 = 0
⇒ r² +6r - 40 = 0
⇒ r² +10r - 4r - 40 = 0
⇒ r(r + 10) - 4(r + 10) = 0
⇒ (r + 10)(r - 4) = 0
 hence  r = 4 cm
r ≠ -10 cm        {∵ length can't be -ve}
Therefore radii of the circles are
r = 4 cm ,
R = 4 + 6 = 10 cm.


Click to let others know, how helpful is it
4.0
44 votes

THANKS
193
Report

Sowmiya35 Expert
hope it help you deat



Click to let others know, how helpful is it
3.0
15 votes

THANKS
41
Report

The BrainAnswerer
Can't find what you're looking for?
ASK YOUR QUESTION

Ask your question

Read more on Brainly.in - https://brainly.in/question/305163#readmore

Answer 2

by this we get radius are 11 and 3. hence this is an answer