Two circle of radii `a and b` touch the axis of `y` on the opposite side at the origin, the former being on the possitive side. Prove that the other two common tangents are given by `(b-a) x+-2sqrt(ab) y-2ab=0`.

Two circles with radii 25 cm and 9 cm touch each other externally. Find the length of the direct common tangent.

Two circles with radii a and b touch each other externally such that theta is the angle between the direct common tangents, (a > bgeq2) . Then prove that theta=2sin^(-1)((a-b)/(a+b)) .

Two circles with radii a and b touch each other externally such that theta is the angle between the direct common tangents, (a > bgeq2) . Then prove that theta=2sin^(-1)((a-b)/(a+b)) .

3 circles of radii a, b, c (a lt b lt c) touch each other externally and have x-axis as a common tangent then

A circle touches y-axis at (0, 2) and has an intercept of 4 units on the positive side of x-axis. The equation of the circle, is

In the figure, two circles touch each other at the point C.Prove that the common tangents to the circles at C, bisect the common tangents at P and Q.

The vertex of an equilateral triangle is (2,3) and the equation of the opposite side is x+y=2 . Then, the other two sides are y-3=(2pmsqrt3)(x-2) .

Tangents are drawn to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,(a > b), and the circle x^2+y^2=a^2 at the points where a common ordinate cuts them (on the same side of the x-axis). Then the greatest acute angle between these tangents is given by (A) tan^(-1)((a-b)/(2sqrt(a b))) (B) tan^(-1)((a+b)/(2sqrt(a b))) (C) tan^(-1)((2a b)/(sqrt(a-b))) (D) tan^(-1)((2a b)/(sqrt(a+b)))

In Figure, two circles touch each other at the point C . Prove that the common tangent to the circles at C , bisects the common tangent at P and Q .

A circle touches the hypotenuse of a right angled triangle at its middle point and passes through the mid-point of the shorter side. If a and b (altb) be the lengths of the sides, then prove that the radius of the circle is b/(4a) sqrt(a^2 + b^2)