NCERT Class 9 Solutions: Circles (Chapter 10) Exercise 10.5 – Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

Get unlimited access to the best preparation resource for IMO-Level-2 : fully solved questions with step-by-step explanation- practice your way to success.

Exterior Angles on Circle- 3 Types of Exteriro Angle Formed …

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)