# NCERT Class 9 Solutions: Circles (Chapter 10) Exercise 10.5 – Part 2

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Q-3 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)

()

Q-4 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,

Q-5 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)