Q4 of 33 Page 51

A rod bent into an angle is placed with its corner at the centre of a circle and it is found that of the circle lies within it. If it is placed with its corner on another circle, what part of the circle would be within it?


The corner of an angle is the centre ‘A’ of a circle. Now extend one side of a angle to meet the circle and join the point to the point where the other side cuts the circle. This gives us half the angle.


Thus,




More from this chapter

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2

The numbers 1, 4, 8 on a clock’s face are joined to make a triangle.


Calculate the angles of this triangle.


How many equilateral triangles can we make by joining numbers on the clock’s face?

 3

In each problem below, draw a circle and a chord to divide it into two parts such that the parts are as specified;

i) All angles on one part 80°.


ii) All angles on one part 110°.


iii) All angles on one part half of all angles on the other.


iv) All angles on one part, one and a half times the angles on the other.

 5

In the picture, O is the centre of the circle and A, B, C are points on it. Prove that ∠ OAC + ∠ ABC = 90°.

 6

Draw a triangle of circumradius 3 centimetres and two of the angles and .