The equation of a circle `S_1` is `x^2 + y^2 = 1`. The orthogonal tangents to `S_1` meet at another circle `S_2` and the orthogonal tangents to `S_2` meet at the third circle `S_3`. Then (A) radius of `S_2 and S_3` are in ratio `1 : sqrt(2)` (B) radius of `S_2 and S_1` are in ratio `1 : 2` (C) the circles `S_1, S_2 and S_3` are concentric (D) none of these

inside the circles x^2+y^2=1 there are three circles of equal radius a tangent to each other and to s the value of a equals to

The equation (s) of circle (s) touching 12x - 5y = 7 at (1, 1) and having radius 13 is/are

A circle S passes through the point (0, 1) and is orthogonal to the circles (x -1)^2 + y^2 = 16 and x^2 + y^2 = 1 . Then (A) radius of S is 8 (B) radius of S is 7 (C) center of S is (-7,1) (D) center of S is (-8,1)

Circle S_(1) is centered at (0,3) with radius 1. Circle S_(2) is externally tangent to circle S_(1) and also tangent to x-axis.If the locus of the centre of the variable circle S_(2) can be expressed as y =1+ ( x^(2))/( lambda) . Find lambda

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

Let S_1 -= x^2 +y^2 - a^2 = 0 and S_2 -= x^2 + y^2 - 2sqrt(2) x - 2 sqrt(2) y-a=0 be two circles. Statement 1 : The value of a for which the circles S_1 = 0 and S_2 = 0 have exactly three common tangents are 0 and 5. Statement 2 : Two circles have exactly 3 common tangents if they touch each other externally. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Find ratio of charges S1 and S2 of they are connected by wire.

A circle S of radius ' a ' is the director circle of another circle S_1,S_1 is the director circle of circle S_2 and so on. If the sum of the radii of all these circle is 2, then the value of ' a ' is (a) 2+sqrt(2) (b) 2-1/(sqrt(2)) (c) 2-sqrt(2) (d) 2+1/(sqrt(2))

If the line y=2-x is tangent to the circle S at the point P(1,1) and circle S is orthogonal to the circle x^2+y^2+2x+2y-2=0 then find the length of tangent drawn from the point (2,2) to the circle S

A circle x^2 +y^2 + 4x-2sqrt2 y + c = 0 is the director circle of circle S_1 and S_1 is the director circle of circle S_2 , and so on. If the sum of radii of all these circles is 2, then find the value of c.