Tangents are drawn to the In -circle of triangle ABC which are prallel to its sides. If x,y,z be the lengths of the tangents and a,b,c be the sides of triangle, then prove that `x/a+y/b+z/c=1`

Tangent at P to the circumcircle of triangle PQR is drawn. If this tangent is parallel to side QR show that Delta PQR is isosceles.

(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

Tangents are drawn from the point (-1, 2) to the parabola y^2 =4x The area of the triangle for tangents and their chord of contact is

Tangents are drawn from the point (-1, 2) to the parabola y^2 =4x The area of the triangle for tangents and their chord of contact is

Let a,b,c be the sides of a triangle ABC, a=2c,cos(A-C)+cos B=1. then the value of C is

If a,b and c are sides of a ritht triangle where c is the hypotenuse, prove that the radius of the circle which touches the sides of the triangle is r = (a + b-c)/(2).

In a right triangle ABC, a circle with AB as diameter is drawn to intersect the hypotenuse AC in P. Prove that the tangent at P, bisects the side BC.

Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base. Given: A triangle A B C in which A B=A C and a circle is drawn by taking A B as diameter which intersects the side B C of triangle at D . To Prove: B D=D C Construction : Join A D .

If the plane x/2+y/3+z/4=1 cuts the coordinate axes in A, B,C, then the area of triangle ABC is

If a,b,c are the sides of a right triangle , where c is the hypotenuse. Prove that the radius r of the circle which touches the sides of the triangle is given by: r=(a+b-c)/2