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 by (1) two secants (2) a secant and a tangent (3) 2 tangents

Exterior Angles on Circle

Exterior angles on circle- 3 types of exteriro angle formed by (1) two secants (2) a secant and a tangent (3) 2 tangents

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

A, B, C are points on a circle with center O, ∠ABC = 100°

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

P, Q, R, S are on circle, ∠ABC = 69°, ∠ ACB = 31°

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.

P, Q, R, S four points on a circle .PQ and SR intersect at a point E,∠SEQ = 130° and ∠EQR = 20°.

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)