Given the base of a triangle and the sum of its sides, prove that the locus of the centre of its incircle is an ellipse.

Prove that the sum of three altitudes drawn from the vertices to opposite sides of a triangle is less than the sum of three sides. or Prove that the perimeter of a triangle is greater than the sum of three altitudes drawn from the vertices to opposite of a triangle.

If a line is drawn parallel to the base of an isosceles triangle to intersect its equal sides, prove that the quadrilateral, so formed is cyclic.

Having given the bases and the sum of the areas of a number of triangles which have a common vertex,show that the locus of the vertex is a straight line.

If on a given base,a triangle be described such that the sum of the tangents of the base angles is a constant,then the locus of the vertex is: (A) a circle (Bi a parabola (C) an ellipse (D) a hyperbola

If two xx the square of the diameter of the circumcircle of a triangle is equal to the sum of the squares of its sides then prove that the triangle is right angled.

If on a given base BC, a triangle is described sungles is m, sum of the that that of the base anples is m, then prove that the locus of the opposite vertex A is a parabola.

Perimeter of a triangle the sum of the lengths of the sides of a triangle is called its perimeter.

Prove that in a quadrilateral the sum of all the sides is greater than the sum of its diagonals.

Each of sides of a triangle is 8cm less than the sum of its other two sides.Area of the triangle ( in cm^(2)) is

The base of an isosceles triangle is 48 cm and one of its equal sides is 30 cm. Find the area of the triangle