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NCERT Class 9 Solutions: Circles (Chapter 10) Exercise 10.5 β Part 2
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, , β , 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)
- , β
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 β SEQ = 130Β° and β EQR = 20Β°. Find β 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)