A relation `R` is defined on the set of circles such that "`C_(1)RC_(2)implies` circle `C_(1)` and circle `C_(2)` touch each other externally", then relation `R` is

ABCD is a square of side length 2 units. C_(1) is the circle touching all the sides of the square ABCD and C_(2) is the circumcircle of square ABCD. L is a fixed line in the same plane and R is fixed point. If a circle is such that it touches the line L and the circle C_(1) externally, such that both the circles are on the same side of the line, then the locus of centre of the circle is

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 C_(1),C_(2),C_(3) with radii r_(1),r_(2),r_(3)(r_(1)ltr_(2)ltr_(3)) respectively are given as r_(1)=2 , and r_(3)=8 they are placed such that C_(2) lines to the right of C_(1) and touches it externally C_(3) lies ot the right of C_(2) and touches it externally. There exist two stratight lines each of whic is a direct common tangent simultaneously to all the three circles then r_(2) is equal to

If C_(1),C_(2),C_(3),... is a sequence of circles such that C_(n+1) is the director circle of C_(n) . If the radius of C_(1) is 'a', then the area bounded by the circles C_(n) and C_(n+1) , is

Show that the relation R defined in the set A of all triangles as R={(T_(1),T_(2)):T_(1) is similar to T_(2) }, is equivalence relation.

The centres of two circles C_(1) and C_(2) each of unit radius are at a distance of 6 unit from each other. Let P be the mid-point of the line segment joining the centres of C_(1) and C_(2) and C be a circle touching circles C_(1) and C_(2) externally. If a common tangent to C_(1) and C passing through P is also a common tangent to C_(2) and C, then the radius of the circle C, is

The centres of two circles C_(1) and C_(2) each of unit radius are at a distance of 6 unit from each other. Let P be the mid-point of the line segment joining the centres of C_(1) and C_(2) and C be a circle touching circles C_(1) and C_(2) externally. If a common tangent to C_(1) and C passing through P is also a common tangent to C_(2) and C, then the radius of the circle C, is

The radical axis of two circles having centres at C_(1) and C_(2) and radii r_(1) and r_(2) is neither intersecting nor touching any of the circles, if

Two circles of radii r_(1) and r_(2), r_(1) gt r_(2) ge2 touch each other externally. If theta be the angle between the direct common tangents, then,

A circle is given by x^2 + (y-1) ^2 = 1 , another circle C touches it externally and also the x-axis, then the locus of center is: