Draw a circle of any radius. Draw diameter PQ. Take 3 points S, T and U any where on the circle. Measure `angle PSQ, angle PTQ and angle PUQ`. What do you observe?

Draw a circle of radius 2.7 cm.Draw a tangent to the circle at any point on it.

Draw a tangent to a circle of radius 3 cm and centre'O' at any point 'K' on the circle.

Draw a circle of radius 3.3 cm.Draw a chord PQ of length 6.6 cm.Draw tangents to the circle at points P and Q.Write your observation about the tangents.

The angle subtended by the diameter at any point on the circles is a//an _______angle.

Let C be the circle with centre (0,0) and radius 3 units. The equation of the locus of the mid-point of the chords of the circle C that subtend an angle of (2pi)/3 at its centre is

Answer the following questions:Make two sufficiently long, identical tubes out of a cardboard. Arrange them on a table, in front of a wall as shown in figure . Place a clock near the end of one of the tubes and try to hear the ticking of the clock at the end of the other tube by placing your ear there. Adjust the angles of the two tubes till you can hear the sound very clearly Measure the angle of incidence theta_1 and the angle of reflection theta_2 . Try to see if they are related in any way. In the experiment, what will happen if you lift one of the tubes to some height?

In the adjoining figure, seg RS is the diameter of the circle with centre 'O'. Point T is in the exterior of the circle. Prove that /_RTS is an acute angle.

A chord PQ of circle with radius 15 cm subtends an angle of 60^@ with the centre of the circle. Find the area of the minor as well as the major segment. (pi =3.14, sqrt3 = 1.73)

In the above figure, seg AB is a diameter of a circle with centre P.C is any point on the circle. Seg CE _|_ seg AB. Prove that CE is the geometric mean of AE and EB. Write the proof with the help of following steps: (a) Draw ray CE. It intersects the circle at D. (b) Show that CE = ED. Write the result using theorem of intersection of chords insides a circle. (d) Using CE = ED, complete the proof.