The centroid of a ∆ABC is G. The area of ∆ABC is 60 cm². The area of ∆GBC is

D, E, F are the mid - points of the sides BC, CA and AB respectively of a ΔABC. Then the ratio of the areas of DEF and ΔABC is D, E, F.

In the given figure, ABCD is a square inscribed in a circle of radius 4 cm. CD is produced till point E. From E a tangent is drawn to the circle at point B.  What is the length (in cm) of AE?

The diagonals AC and BD of a cyclic quadrilateral ABCD intersect each other at the point P. Then, it is always true that 

The radius of the circumcircle of a right-angled triangle is 15 cm and the radius of its in circle is 6 cm. Find the sides of the triangle. 

A solid sphere of diameter 7 cm is cut into two equal halves. What will be the increase (in cm.²) in the total surface area?

In triangle ABC a straight line parallel to BC intersects AB and AC at D and E respectively. If AB = 2AD then DE : BC is

If two complementary angles are in the ratio of 2:3. find the ratio of square of smaller angle to square of greater?