Suppose you are given a circle. Give a construction to find its centre.

Suppose you are incharge of a grain store. How will you find out the presence of pests ? Mention any two indications.

Draw any circle and mark: its centre

Show that the points A(1, 0), B(2, -7), C(8, 1) and D(9,-6) all lie on the same circle. Find the equation of this circle, its centre and radius.

A chord 6 cm long is drawn in a circle with a diameter equal to 10 cm. Find its perpendicular distance from the centre.

Find the equations of the following curves in cartesian form. Wherever the curve is a circle, find its centre and radius : x= at^2, y=2at .

Show that the four points of intersection of the lines : (2x-y + 1) (x-2y+3) = 0 , with the axes lie on a circle and find its centre.

Suppose you drop a die at random on the rectangular region shown in Fig. What is the probability that it will land inside the circle with diameter 1 m ?