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

The ends of hypotenuse of a right angled triangle are (a,0),(-a,0) then the locus of third vertex is

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

Find the locus of the vertex of a triangle with fixed base and having constant area

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.

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