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[" 10.(i) If the bisector of the angle "A" of triangle "ABC" meets "BC" in "D" ,prove that "],[qquad a=(b+c)[1-(AD^(2))/(bc)]^(1/2)],[" (ii) If the tangents of the angles of a triangle are in A.P.,prove that the squares of the sides are in "],[" the ratio "x^(2)(x^(2)+9):(3+x^(2))^(2):9(1+x^(2))," where "x" is tangent of the least or the greatest angle."]

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