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?

PAB and PCD are two secants to a circle . If PA 10 cm , AB = 12 cm and PC = 11 cm , then what is the value ( in cm ) of PD ?

If one of the equal angles of an isosceles triangle is 65°, then the angle at the vertex is

The ratio of circumradius and hypotenuse a right-angled triangle is

The ratio between the number of sides of two regular polygons is 1 : 2 and the ratio between there interior angles is 2 : 3. The number of sides of these polygons is respectively 

The lengths of the lengths placed on the sides of a point inside an equilateral triangle are 6 cm, 8 cm and 10 cm. What is the area of the triangle?

Triangle PQR is inscribed in a circle such that P, Q and R lies on the circumference . If PQ is the diameter of the circle and ∠PQR = 40 ° , then what is the value ( in degrees ) of ∠QPR ?

A sector area of 4%   is removed from a circular sheet of paper of diameter 50 cm, If the remaining part is used to make a conical surface , then the ratio of radius and height of the-