Let ABC be a triangle and a circle `C_1` drawn lying inside the triangle touching its incircle `C_2` externally and also touching its two sides AB and AC. Show that the ratio of radii of the circles `C_1` and `C_2` is equal to `tan^2((pi-A)/4)`

The radius of the circle touching two sides AB and AC of a triangle ABC and having its center on BC is equal to………………..

Consider circles C_(1) and C_(2) touching both the axes and passing through (4, 4), then the product of the radii of the two circles is

A circle 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 :

(c) 103 (d) 10 18. A circle is inscribed in an equilateral triangle with side lengths 6 unit. Another circle is drawn inside the triangle (but outside the first circle), tangent to the first circle and two of the sides of the triangle. The radius of the smaller circle is (b) 2/3 (a) 1/ root3 (c) 2 (d) 1

In Delta ABC, angle A = (pi)/(3) and its incircle of unit radius. Find the radius of the circle touching the sides AB, AC internally and the incircle of Delta ABC externally is x , then the value of x is

Let C_1 and C_2 be two circles with C_2 lying inside C_1 A circle C lying inside C_1 touches C_1 internally and C_2 externally. Identify the locus of the centre of C

Let A B C be a triangle right-angled at Aa n dS be its circumcircle. Let S_1 be the circle touching the lines A B and A C and the circle S internally. Further, let S_2 be the circle touching the lines A B and A C produced and the circle S externally. If r_1 and r_2 are the radii of the circles S_1 and S_2 , respectively, show that r_1r_2=4 area ( A B C)dot

A circumcircle is a circle which passes through all vertices of a triangle and an incircle is a circle which is inscribed in a triangle touching all sides of a triangle. Let ABC be a right-angled triangle whose radius of the circumcircle is 5 and its one side AB = 6. The radius of incircle of triangle ABC is r. Area of Delta ABC is

A circumcircle is a circle which passes through all vertices of a triangle and an incircle is a circle which is inscribed in a triangle touching all sides of a triangle. Let ABC be a right angled triangle whose radius of circumcircle is 5 and its one side AB = 6. The radius of incircle of triangle ABC is r. The value of r is

In a triangle ABC, prove that the ratio of the area of the incircle to that of the triangle is pi:cot(A/2) cot(B/2) cot(C/2)