In triangle ABC, ∠BAC = 90°, AB = 6 cm and BC = 10 cm. A circle is drawn inside the triangle which touches all the sides of the triangle (i.e. an incircle of △ABC is drawn). Find the area of the triangle excluding the circle.

A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides it is just immersed . What fraction of water overflows ?

Solve for x ∈ W, 0° ≤ x ≤ 90°.

(i) 3 tan² 2x = 1

(ii) tan² x = 3(sec x - 1)