A triangle is circumscribed on the circle of centre O in such a way that sides AB = 12 cm, BQ = 7 cm and CQ = 5 cm. Calculate the lengtth (in cm) of side AC.
Calculate the length (in cm) of PQ, if the radius of the circle is 7 cm and the line through the centre O meets the tangent at point Q such that OP = 25 cm.
The volume of a right circular cone, with a base radius the same as its altitude, and the volume of a hemisphere are equal. The ratio of the radii of the cone to the hemisphere is
The difference between Charles' and Shriya's ages is 6 years. When they married each other 30 years ago, 4 times Charle's age was the same as 5 times the age of Shriya. What is the current sum of their ages?