If base of triangle and ratio of tangent...

If base of triangle and ratio of tangents of half of the base angles are given, then prove that the locus opposite vertex is hyperbola.

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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 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.

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write the ratio of the angles of an equilateral triangle.

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The base of a triangle is divided into three equal parts. If t_1, t_2,t_3 are the tangents of the angles subtended by these parts at the opposite vertex, prove that (1/(t_1)+1/(t_2))(1/(t_2)+1/(t_3))=4(1+1/(t2 2))dot

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