Two medians AD and BE of ∆ABC intersect G at right angle. If AD = 9 cm and BE = 6 cm, then the length of BD ( in cm ) is

Two equal circles of radius 4 cm intersect each other such that each passes through the center of the other. The length of the common chord is

In ΔABC, AB = AC and ∠B = 40 °, find the value of ∠A.

In a triangle ΔABC, the sides DE parallel to BC and AD = 6 cm, DB = 9 cm, AE = 8 cm, find the value of AC.

 If $$ {x=7-4\sqrt{3}}$$ find the value of $$ {\sqrt{x}+{1\over {\sqrt{x}}}}$$.

A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. The area of the circle is:

The sum of all interior angles of a regular polygon is twice the sum of all its exterior angles.  The number of sides of the polygon is

The area of a circle is proportional to the square of its radius. A small circle of radius 3 cm is drawn within a larger circle of radius 5 cm. Find the ratio of the difference between the area of the larger circle and that of the smaller circle to the area of the larger circle.