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

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Exterior angles on circle- 3 types of exteriro angle formed …

Exterior Angles on Circle

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Q-3 In the figure, where A, B and C are points on a circle with centre O. Find

A, B, C Are Points on a Circle with Center O

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

Points P, Q, R, S on Circle

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.

P, Q, R, S Four Points on a Circle

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)