Circle Properties and Terminology
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Circle Properties and Terminology — Free MYP2 Mathematics Practice Questions

1QuestionDrawing Circles with Compass and RulerConcept Practice
2 marks~3 minCriterion A
The diagram shows a circle with centre OO. Point PP lies on the circumference. Line segment OPOP is drawn.
a
Identify the mathematical name of line segment OPOP. [1]
b
Measure the length of OPOP on the diagram and state your answer in centimetres. [1]
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Solutions

2QuestionSymmetry and Angle Properties in CirclesAssessment Practice
3 marks~5 minCriterion C
In the diagram, OO is the centre of a circle. Points AA, BB, and CC lie on the circumference. Angle AOB=80°AOB = 80°.
a
Identify the type of angle that ∠ACB\angle ACB is. [1]
b
Calculate the measure of ∠ACB\angle ACB. [1]
c
A classmate says: "If CC were moved to a different position on the same arc, ∠ACB\angle ACB would change." Explain whether your classmate is correct. [1]
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Solutions

3QuestionExploring Tangents and Secants IntroductoryAssessment Practice
6 marks~9 minCriterion B
A tangent and a secant meet at a point on a circle. The table shows the intercepted arc (the arc cut off between the two points where the secant crosses the circle) and the angle between the tangent and secant.

Intercepted arc: 60°, 90°, 120°, 150°60°,\ 90°,\ 120°,\ 150°
Angle: 30°, 45°, 60°, 75°30°,\ 45°,\ 60°,\ 75°
a
State the relationship between the angle and the intercepted arc. [1]
b
Explain how you would find the angle when the intercepted arc is 160°160°. Show your working. [2]
c
A classmate says: "The angle equals the intercepted arc because both come from the same arc." Compare this claim with the inscribed angle theorem (an inscribed angle equals half its intercepted arc) and explain whether your classmate is correct. [3]
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Solutions

4QuestionUnderstanding Central Angle and CircumferenceAssessment Practice
6 marks~9 minCriterion D
A sports centre is designing a circular running track with a radius of 50 m. A sector (a "pizza-slice" region) is marked with a central angle of 72°. Use π=3.14\pi = 3.14.
a
Calculate the arc length of the sector. [2]
b
Explain why the formula Arc Length=angle360×2πr\text{Arc Length} = \dfrac{\text{angle}}{360} \times 2\pi r only works when the angle is measured in degrees. [2]
c
State one limitation of using this formula to design a real running track, and explain how it could affect the build. [2]
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Solutions

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