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 the base of a triangle and the ratio of the lengths of the other two unequal sides are given, then the vertex lies on

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.

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.

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

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.

Let the base of a triangle lie along the line x = a and be of length a. The area of this triangles is a^(2) , if the vertex lies on the line

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.

To construct a triangle, given its perimeter and its two base angles.

A square is incribed in an isoceles right triangle, so that the square and the triangle have one angle common. Show that the vertex of the sqare opposite the vertex of the common angle bisects the hypotenuse.