Two circles touch internally. The sum of their areas is116 cm² and the distance between their centres is 6cm. Find the radii of the circles.
Answers
Answered by
3
π×r²+π×R² = 116
22/7(r²+R²) = 116
r²+R² = (58×7)÷11
r+R = 6
r = 6-R
36+R²-12R+R² = 406/11
R²-6R+18 = 203/11
11R²-66R+198-203 = 0
11R²-66R-5 = 0
R = (66±√4136)÷22
= (33±√1034)÷11
hope it helped you a lot
please mark it as the brainliest answer
22/7(r²+R²) = 116
r²+R² = (58×7)÷11
r+R = 6
r = 6-R
36+R²-12R+R² = 406/11
R²-6R+18 = 203/11
11R²-66R+198-203 = 0
11R²-66R-5 = 0
R = (66±√4136)÷22
= (33±√1034)÷11
hope it helped you a lot
please mark it as the brainliest answer
Answered by
8
Answer:
Step-by-step explanation:
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.
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