Circle Geometry Quiz for Class IX Students

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

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

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

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

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

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.

Test your knowledge of circles in geometry with this quiz for Class IX students. Solve problems related to diameters, radii, and angles in circles to sharpen your geometry skills.