A secant PAB is drawn from an external point P to the circle with centre O, intersecting it at A and B. If OP = 17 cm, PA = 12 cm and PB = 22.5 cm, then the radius of the circle 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.

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

If ABCDEF is a regular hexagon, then what is the value (in degrees) of ∠ADB? 

O is the orthocentre of ΔABC. If ∠BOC=110°, ∠BAC is equal to

PQRS is square whose side is 20 cm. By joining opposite vertices of PQRS are get four triangles. What is the sum of the perimeters of the four triangles?

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

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