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