Advertisements
Advertisements
प्रश्न
Two circles touch each other externally. The sum of their areas is 58πcm2 and the distance between their centres us 10cm. Find the radii of the two circles.
Advertisements
उत्तर
Let one of the two circles touching externally have a radius of R and the other have radius r
Given R + r = 10cm.
So, R = 10 - r
The Area of a Circle with radius r = πr2
The Area of a Circle with radius R = πR2
Sum of the areas of the two circles
= πr2 + πR
= π(r2 + R2)
= 58π
⇒ r2 + R2 = 58
⇒ r2 + (10 - r)2 = 58
⇒ r2 + 100 + r2 - 20r = 58
⇒ 2r2 - 20r + 42 = 0
⇒ r2 - 10r + 21 = 0
⇒ r2 - 7r - 3r + 21 = 0
⇒ r(r - 7) -3(r - 7) = 0
⇒ (r - 7)(r - 3) = 0
⇒ r = 7, 3
So, one of the two circles touching externally has a radius of 7cm and the other have radius 3cm.
APPEARS IN
संबंधित प्रश्न
In the given figure ABCD is quadrilateral in which diagonal BD = 24 cm, AL ⊥ BD and CM ⊥ BD such that AL = 9cm and CM = 12 cm. Calculate the area of the quadrilateral.
Find the area enclosed between two concentric circles of radii 3.5 cm and 7 cm. A third concentric circle is drawn outside the 7 cm circle , such that the area enclosed between it and the 7 cm circle is same as that between the two inner circles . Find the radius of the third circle correct to one decimal place.
What is the area of a sector of a circle of radius 5 cm formed by an arc of length 3.5 cm?
If the circumference and the area of a circle are numerically equal, then diameter of the circle is
The perimeter of the sector OAB shown in the following figure, is
The area of a sector whose perimeter is four times its radius r units, is
The radii of two circles are 8 cm and 6 cm. Find the radius of the circle having area equal to the sum of the areas of the two circles.
Find the radius and area of a circle, whose circumference is :
(i) 132 cm
(ii) 22 m
The radii of two circles are in the ratio 5 : 8. If the difference between their areas is 156p cm2, find the area of the bigger circle.
The circumference of a circular park is 352 m. Find the area of the park
