1

### IIT-JEE 1984

Subjective
With usual notation, if in a triangle $$ABC$$;
$${{b + c} \over {11}} = {{c + a} \over {12}} = {{a + b} \over {13}}$$ then prove that $${{\cos A} \over 7} = {{\cos B} \over {19}} = {{\cos C} \over {25}}$$.

Solve it.
2

### IIT-JEE 1984

Subjective
For a triangle $$ABC$$ it is given that $$\cos A + \cos B + \cos C = {3 \over 2}$$. Prove that the triangle is equilateral.

Solve it.
3

### IIT-JEE 1983

Subjective
The ex-radii $${r_1},{r_2},{r_3}$$ of $$\Delta$$$$ABC$$ are H.P. Show that its sides $$a, b, c$$ are in A.P.

Solve it.
4

### IIT-JEE 1982

Subjective
A vertical pole stands at a point $$Q$$ on a horizontal ground. $$A$$ and $$B$$ are points on the ground, $$d$$ meters apart. The pole subtends angles $$\alpha$$ and $$\beta$$ at $$A$$ and $$B$$ respectively. $$AB$$ subtends an angle $$\gamma$$ and $$Q$$. Find the height of the pole.

$${d \over {\sqrt {{{\cot }^2}\alpha + {{\cot }^2}\beta - \cot \alpha \cot \beta \cot \gamma } }}$$

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