Three circles touch each other externally. The tangents at their point of contact meet at a point whose distance from a point of contact is 4. Then, the ratio of their product of radii to the sum of the radii is

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

The point of contact of y^(2) = 4ax and the tangent y = mx +c is

Find the points of contact Q and R of a tangent from the point P(2,3) on the parabola y^2=4xdot

The x-intercept of the tangent to a curve is equal to the ordinate of the point of contact. The equation of the curve through the point (1,1) is

The tangent at any point on the curve x = at^3. y = at^4 divides the abscissa of the point of contact in the ratio m:n, then |n + m| is equal to (m and n are co-prime)

The curve xy = c(c > 0) and the circle x^2 +y^2=1 touch at two points, then distance between the points of contact is

Find the area of the triangle formed by the tangents from the point (4, 3) to the circle x^2+y^2=9 and the line joining their points of contact.

The circles which are not congruent touch externally. The sum of their areas is 130picm^(2) and distance between their centres is 14 cm . Find the radii of the two circles.

The perpendicular from the origin to the tangent at any point on a curve is equal to the abscissa of the point of contact. Also curve passes through the point (1,1). Then the length of intercept of the curve on the x-axis is__________