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1

### IIT-JEE 1985

Subjective
In a triangle $$ABC$$, the median to the side $$BC$$ is of length $${1 \over {\sqrt {11 - 6\sqrt 3 } }}$$\$ and it divides the angle $$A$$ into angles $${30^ \circ }$$ and $${45^ \circ }$$. Find the length of the side $$BC$$.

$$2$$ units.
2

### IIT-JEE 1985

Subjective
A ladder rests against a wall at an angle $$\alpha$$ to the horizintal. Its foot is pulled away from the wall through a distance $$a$$, so that it slides $$a$$ distance $$b$$ down the wall making an angle $$\beta$$ with the horizontal. Show that $$a = b\tan {1 \over 2}\left( {\alpha + \beta } \right)$$

Solve it.
3

### 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.
4

### 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.

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