Q3 In the figure, where A, B and C are points on a circle with centre O. Find
Solution:
The major arc AC subtends an angle AOC at the center and an angle ABC on rest of the circle. Therefore,
(the angle inside the quadrilateral ABCO).
In , (radius of the circle), therefore the triangle is isosceles and hence,
Now,
Q4 In the figure,, ∠ , find
Solution:
Given
Note that, (Angles subtended by the same segment on the circle)
In
Thus,
Q5 In the figure, P, Q, R and S are four points on a circle. PQ and SR intersect at a point E such that ∠SEQ = 130° and ∠EQR = 20°. Find ∠ SPQ.
Solution:
Given,

P, Q, R, S are four points on a circle.

PQ and SR intersect at a point E

(Angles in the segment of the circle)
In ,
So, ) (Angles subtended by the same arc)