If the circumradius of an equilateral triangle ABC is 8 cm, then what is the height of the triangle?

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.

If ABC is an equilateral triangle and P, Q, R respectively denote the middle points of AB, BC, CA, then 

The exterior angle of a regular polygon is one-third of its interior angle, the number of sides of the polygon is -

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 length of a chord which is at a distance of 12 cm from the center of a circle of radius 13 cm is 

ABC is an isosceles triangle with AB = AC, A circle through B touching AC at the middle point of Q, intersects AB at P. Then AP : AB is : 

∆ABC is a right angle triangle BD⊥AC. If AD = 12 cm and DC = 8, then BD = ?