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1

### IIT-JEE 1980

Subjective
(i) $$PQ$$ is a vertical tower. $$P$$ is the foot and $$Q$$ is the top of the tower. $$A, B, C$$ are three points in the horizontal plane through $$P$$. The angles of elevation of $$Q$$ from $$A$$, $$B$$, $$C$$ are equal, and each is equal to $$\theta$$. The sides of the triangle $$ABC$$ are $$a, b, c$$; and the area of the triangle $$ABC$$ is $$\Delta$$. Show that the height of the tower is $${{abc\tan \theta } \over {4\Delta }}$$.

(ii) $$AB$$ is vertical pole. The end $$A$$ is on the level ground. $$C$$ is the middle point of $$AB$$. $$P$$ is a point on the level ground. The portion $$CB$$ subtends an angle $$\beta$$ at $$P$$. If $$AP = n\,AB,$$ then show that tan$$\beta$$ $$= {n \over {2{n^2} + 1}}$$

(i) Solve it.

(ii) Solve it.

2

Subjective

Solve it.
4

### IIT-JEE 1979

Subjective
(a) If a circle is inscribed in a right angled triangle $$ABC$$ with the right angle at $$B$$, show that the diameter of the circle is equal to $$AB+BC-AC$$.

(b) If a triangle is inscribed in a circle, then the product of any two sides of the triangle is equal to the product of the diameter and the perpendicular distance of the third side from the opposite vertex. Prove the above statement.

Solve it.

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