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

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 Equation , where A, B and C are points on a circle with centre O. Find Equation

Circle c Circle c: Circle through C with center O Angle ? Angle ?: Angle between A, B, A' Angle ? Angle ?: Angle between A, B, A' Angle ? Angle ?: Angle between A, B, A' Segment f Segment f: Segment [C, A] Segment g Segment g: Segment [A, B] Segment h Segment h: Segment [B, C] Segment i Segment i: Segment [A, O] Segment j Segment j: Segment [C, O] Point O O = (0.16, 2.66) Point O O = (0.16, 2.66) Point O O = (0.16, 2.66) Point C C = (2.58, 3.06) Point C C = (2.58, 3.06) Point C C = (2.58, 3.06) Point A Point A: Point on c Point A Point A: Point on c Point A Point A: Point on c Point B Point B: Point on c Point B Point B: Point on c Point B Point B: Point on c

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

  • Equation

The major arc AC subtends an angle AOC at the center and an angle ABC on rest of the circle. Therefore,

Equation

Equation (the angle inside the quadrilateral ABCO).

In Equation , Equation (radius of the circle), therefore the triangle is isosceles and hence, Equation

Now,

  • Equation (Sum of the angles in triangle)

  • Equation ( Equation )

  • Equation

  • Equation

Q-4 In the figure, Equation , ∠ Equation , find Equation

Circle c Circle c: Circle through R with center A Angle ? Angle ?: Angle between P, Q, R Angle ? Angle ?: Angle between P, Q, R Angle ? Angle ?: Angle between P, Q, R Angle ? Angle ?: Angle between P, R, Q Angle ? Angle ?: Angle between P, R, Q Angle ? Angle ?: Angle between P, R, Q Segment f Segment f: Segment [Q, R] Segment g Segment g: Segment [Q, S] Segment h Segment h: Segment [S, R] Segment i Segment i: Segment [R, P] Segment j Segment j: Segment [P, Q] Point R R = (2.52, 3) Point R R = (2.52, 3) Point R R = (2.52, 3) Point Q Point Q: Point on c Point Q Point Q: Point on c Point Q Point Q: Point on c Point S Point S: Point on c Point S Point S: Point on c Point S Point S: Point on c Point P Point P: Point on c Point P Point P: Point on c Point P Point P: Point on c

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

  • Equation , Equation

Note that, Equation (Angles subtended by the same segment on the circle)

In Equation

  • Equation (Sum of the angles on a triangle)

  • Equation Equation , ∠ Equation

  • Equation

  • Equation

Thus, Equation

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.

Circle c Circle c: Circle through B with center A Angle ? Angle ?: Angle between S, E, C' Angle ? Angle ?: Angle between S, E, C' Angle ? Angle ?: Angle between S, E, C' Angle ? Angle ?: Angle between R, Q, F' Angle ? Angle ?: Angle between R, Q, F' Angle ? Angle ?: Angle between R, Q, F' Segment f Segment f: Segment [S, Q] Segment g Segment g: Segment [S, E] Segment h Segment h: Segment [E, Q] Segment i Segment i: Segment [R, Q] Segment j Segment j: Segment [R, S] Segment k Segment k: Segment [P, E] Segment l Segment l: Segment [P, S] Point S Point S: Point on c Point S Point S: Point on c Point S Point S: Point on c Point Q Point Q: Point on c Point Q Point Q: Point on c Point Q Point Q: Point on c Point E E = (-0.11, 5.34) Point E E = (-0.11, 5.34) Point E E = (-0.11, 5.34) Point R Point R: Point on c Point R Point R: Point on c Point R Point R: Point on c Point P Point P: Point on c Point P Point P: Point on c Point P Point P: Point on c

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

  • Equation (Angles in the segment of the circle)

In Equation ,

  • Equation (Exterior angles of the triangle)

  • Equation

  • Equation

So, Equation Equation ) (Angles subtended by the same arc)

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