What happen if the angle in the circle segment is right angle? What kind of segment do you obtain? Draw the figure and give reason.

(a) Figure 9.32 shows a cross-section of a 'light pipe' made of a glass fibre of refractive index 1.68. The outer covering of the pipe is made of a material of refractive index 1.44. What is the range of the angles of the incident rays with the axis of the pipe for which total reflections inside the pipe take place, as shown in the figure. (b) What is the answer if there is no outer covering of the pipe?

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line -segment joinig the point of contact at the centre.

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line - segment joining the points of contact at the centre.

If one of the sides and any other part (either an acute angle or any side) of a right angle triangle is known, the remaining sides and angles of the triangle can be determined. Do you agree? Explain with an example.

What is the measure of angleA + angleB + angleC + angleD + angleE + angleF in the figure given below. Give reason to your answer.

Look at the drawing given in the figure which has been drawn with ink of uniform line-thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments is m. The mass of the ink used to draw the outer circle is 6 m. The coordinates of the centres of the different parts are: outer cicle (0,0), left circle (-a, a), right inner circle (a,a), vertical line (0,0) and horizontal line (0 ,-a). The y-coordinate of the centre of mass of the ink in this drawing is