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.

Given the base BC of the triangle ABC and if angleC-angleB=k, a constant, show that the locus of the vertex A is a hyperbola.

If two isosceles triangles have a common base, prove that the line joining their vertices bisects them at right angles.

If two isosceles triangles have a common base, prove that the line joining their vertices bisects them at right angles.

The locus of vertices of all isosceles triangles having a common base.

If on a given base B C , a triangle is described such that the sum of the tangents of the base angles is m , then prove that the locus of the opposite vertex A is a parabola.

The number of lines of symmetry which a triangle cannot have is

If the base of a triangle and the ratio of tangent of half of base angles are given, then identify the locus of the opposite vertex.

If the base of a triangle and the ratio of tangent of half of base angles are given, then identify the locus of the opposite vertex.

The ends of the hypertenuse of right angled triangle are ( 0 , 6 ) , (6, 0 ) . The locus of the third vertex is

One vertex of a triangle of given species is fixed and another moves along circumference of a fixed circle. Prove that the locus of the remaining vertex is a circle and find its radius.