PQR is an equilateral triangle whose side is 10 cm . What is the value (in cm) of the inradius of triangle PQR ?

AB is diameter of a circle with centre 'O'. CD is a chord which is equal to the radius of the circle. AC and BD are extended so that they intersect each other at point P. Then find the value of ∠ APB.

If in a triangle, the orthocenter lies on vertex, then the triangle is 

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?

If the ratio of the measurement of the four angles of a quadrilateral is 1: 2: 3: 4, then the measurement of its smallest angle is-

ABCD is a rhombus whose one angle is 60°.Find the ratio of the lengths of its diagonal?

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

ΔABC and ΔDBC are on the same base BC but on opposite sides of it. AD and BC intersect each other O. If AO=a cm, DO=b cm and the area of ΔABC= x cm², then what is the area (in cm²) of ΔDBC?