Circle Geometry Quiz for Class IX Students

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Questions and Answers

In a circle with a radius of 17cm, if AB is 30cm, what is the distance of AB from the center?

13 cm

In figure 1, if ∠𝑂𝐴𝐵 = 350, what is the value of ∠𝐴𝐶𝐵?

70 degrees

In figure 2, if ∠BAO= 60 degrees and BC is the diameter of the circle, what is the value of ∠ADC?

30 degrees

In figure 3, if ∠AEC is 80 degrees, what is the value of reflex ∠AOC?

<p>280 degrees</p> Signup and view all the answers

In figure 4, if ∠OAB = 20 degrees and ∠OCB = 55 degrees, what are the values of ∠BOC and ∠AOC?

<p>110 degrees and 70 degrees, respectively</p> Signup and view all the answers

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Study Notes

Circle Properties and Theorems

  • A circle has a diameter, which is a line that passes through the center of the circle.
  • A circle has a radius, which is the distance from the center of the circle to any point on the circle.

Problems and Solutions

  • If AD is the diameter of a circle of radius 17cm and AB is of length 30 cm, the distance of AB from the center can be found.
  • If ∠OAB = 200 and ∠OCB = 550, then ∠BOC and ∠AOC can be found.
  • In a circle, if ∠OAB = 200, then ∠BOC = 140 and ∠AOC = 340.
  • If ∠PQR = 650 and ∠SPR = 400, then ∠QPR, ∠PRS, and ∠SOR can be found.

Angles and Chords

  • If ∠OAB = 200, then ∠BOC = 140 and ∠AOC = 340.
  • If AB and CD are two parallel chords of a circle, which are on opposite sides of the center, the radius of the circle can be found.
  • If AB = 10 cm and CD = 24 cm, and the distance between the chords is 17 cm, the radius of the circle can be found.

Circle Theorems

  • If ∠XOZ = 2( ∠XZY + ∠YXZ ), then XOZ is an isosceles triangle.
  • If ∠OAB = 200, then ∠BOC = 140 and ∠AOC = 340.

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