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 the lengths of the other two unequal sides are given, then the vertex lies on

Given the base of a triangle and the ratio of the tangent of half the base angles .Show that the vertex moves on a hyperbola whose foci are the extremities of a diameter

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.

If on a given base BC[B(0,0) and C(2,0)], a triangle is described such that the sum of the base angles is 4, then the equation of the locus of the opposite vertex A is parabola whose directrix is y=k. The value of k is _________ .

Statement 1 : Given the base B C of the triangle and the radius ratio of the excircle opposite to the angles Ba n dCdot Then the locus of the vertex A is a hyperbola. Statement 2 : |S P-S P|=2a , where Sa n dS ' are the two foci 2a is the length of the transvers axis, and P is any point on the hyperbola.

In a Delta ABC the tangent of half the difference of two angles is one thired the tangement of half the sum of the angles .Determine the ratio of the sides opposite to the angles .

In a DeltaABC, the tangent of hald the difference of two angle is one-third the tangent of half the sum of the angle. Determine the ratio of the sides opposite to the angles.

Find the angles of an isoscles triangles, if the ratio of the base angle to the vertical angle is 2: 5

The exterior angles of a triangle is 130^(@) and the two interior opposite angle are in the ratio 6:7. find the angles of the triangle.

One angle of a triangle is equal to one angle of another triangle and the bisectors of these two equal angles divide the opposite sides in the same ratio, prove that the triangles are similar.