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 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

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

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

If two circles touch each other (internally or externally); the point of contact lies on the line through the centres.