NCERT Class 9 Solutions: Circles (Chapter 10) Exercise 10.5 – Part 2
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Q3 In the figure, where A, B and C are points on a circle with centre O. Find
Solution:

Given A, B, and C are points on a circle with center O

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,

(Sum of the angles in triangle)

()


Q4 In the figure,, ∠ , find
Solution:
Given

P, Q, R, and S are points on a the circle

,
Note that, (Angles subtended by the same segment on the circle)
In

(Sum of the angles on a triangle)

, ∠


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 ,

(Exterior angles of the triangle)


So, ) (Angles subtended by the same arc)