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

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

The length of the common chord of two circles of radii 30 cm and 40 cm whose centers are 50 cm apart is (in cm) 

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

If there are four lines in a plane, then what cannot be the number of points of intersection of these lines? 

In ΔABC, ∠C=90° and D is a point on CB such that AD is the bisector of ∠A. If AC=5 cm and BC=12 cm, then what is the length of AD?

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:

If the perimeter of an equilateral triangle is 30 meters, what is its height?