Three circles whose radii are a,b and c and c touch one other externally and the tangents at their points of contact meet in a point. Prove that the distance of this point from either of their points of contact is `((abc)/(a+b+c))^(1/2)`.

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

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

Three circles with radius r_(1), r_(2), r_(3) touch one another externally. The tangents at their point of contact meet at a point whose distance from a point of contact is 2 . The value of ((r_(1)r_(2)r_(3))/(r_(1)+r_(2)+r_(3))) is equal to

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

Circles with radii 3, 4 and 5 touch each other externally. If P is the point of intersection of tangents to these circles at their points of contact, then if the distance of P from the points of contact is lambda then lambda_2 is _____

Circles of radii 3,4,5 touch each other externally . Let P be the point of intersection of tangents of these circles at their points of contact .Show that the distance of P from a point of contact is sqrt5 .

Two circles touch each other externally at point P. Q is a point on the common tangent through P. Prove that the tangents QA and QB are equal.

Prove that the tangent at any point of circle is perpendicular to the radius through the point of contact.

Prove that the tangent at any point of circle is perpendicular to the radius through the point of contact.

If a circle, whose centre is (-1,1) touches the straight line x+2y = 12, then the co-ordinates of the point of contact are