If the sum of the areas of two circles with radii `r_1` and `r_2` is equal to the area of a circle of radius `r`, then `r_1^2 +r_2^2` (a) `> r^2` (b) `=r^2` (c) `

If the sum of the circumferences of two circles with radii R_(1) and R_(2) is equal to the circumference of a circle of radius R, then

The length of the common chord of two circles of radii r_1 and r_2 which intersect at right angles is

The circles having radii r_1 and r_2 intersect orthogonally. Find the length of their common chord.

The area of a circle is given by A= pi r^(2) , where r is the radius. Calculate the rate of increase of area w.r.t radius.

Two circles of radii r_1 and r_2 , are both touching the coordinate axes and intersecting each other orthogonally. The value of r_1/r_2 (where r_1 > r_2 ) equals -

Angle of intersection of two circle having distance between their centres d is given by : (A) cos theta = (r_1^2 + r_2^2 - d)/(2r_1^2 + r_2^2) (B) sec theta = (r_1^2 + r_2^2 + d^2)/(2r_1 r_2) (C) sec theta = (2r_1 r_2)/(r_1^2 + r_2^2 - d^2 (D) none of these

If S_1=x^2+y^2+2g_1x+2f_1y+c_1=0 and S_2=x^2+y^2+2g_2x +2f_2y+c_2=0 are two circles with radii r_1 and r_2 respectively, show that the points at which the circles subtend equal angles lie on the circle S_1/r_1^2=S_2/r_2^2

Let A B C be a triangle right-angled at Aa n dS be its circumcircle. Let S_1 be the circle touching the lines A B and A C and the circle S internally. Further, let S_2 be the circle touching the lines A B and A C produced and the circle S externally. If r_1 and r_2 are the radii of the circles S_1 and S_2 , respectively, show that r_1r_2=4 area ( A B C)dot

Prove that if two bubbles of radii r_(1) and r_(2) coalesce isothermally in vacuum then the radius of new bubble will be r=sqrt(r_(1)^(2)+r_(2)^(2))

The areas of two circles are in a ratio of 4:9. If both radii are integers and r_(1)-r_(2)=2 , which of the following is the radius of the larger circle?