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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?
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?
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?
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?
In figure 3, if ∠AEC is 80 degrees, what is the value of reflex ∠AOC?
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In figure 4, if ∠OAB = 20 degrees and ∠OCB = 55 degrees, what are the values of ∠BOC and ∠AOC?
In figure 4, if ∠OAB = 20 degrees and ∠OCB = 55 degrees, what are the values of ∠BOC and ∠AOC?
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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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