Grade 9 · Math · Unit 7 of 11
Circle Properties
Chords, tangents, and inscribed and central angles.
What your child practises
Practises circle properties: the perpendicular from the centre bisects a chord, central angles are twice inscribed angles on the same arc, inscribed angles on the same arc are equal, and a tangent is perpendicular to the radius.
Manitoba Curriculum learning outcome: 9.SS.1 · circle properties: chords, central and inscribed angles, and tangents
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
Which line is perpendicular to the radius where it touches the circle?
- the tangent
- the arc
- the chord
Show answer
the tangent
Hint: The tangent and the radius meet at 90°.
Question 2
A diameter is a chord that…
- is shorter than the radius
- touches the circle once
- passes through the centre
Show answer
passes through the centre
Hint: It is the longest possible chord.
Question 3
Which statement about the central angle is true?
- It is always 90°
- Its vertex is on the circle
- Its vertex is at the centre of the circle
Show answer
Its vertex is at the centre of the circle
Hint: An inscribed angle has its vertex on the circle.
Question 4
A tangent touches a circle at point P. The angle between the tangent and the radius to P is…
- 90°
- 180°
- 45°
Show answer
90°
Hint: A tangent is perpendicular to the radius at the point of tangency.
Question 5
Which of these is true for inscribed angles on the same arc?
- They add to 90°
- They are each twice the radius
- They are congruent
Show answer
They are congruent
Hint: Congruent means equal in measure.
Question 6
A circle has a radius of 6 cm. A tangent segment runs from an outside point to the circle, and that point is 10 cm from the centre. How long is the tangent segment?
- 16 cm
- 4 cm
- 8 cm
Show answer
8 cm
Hint: The tangent meets the radius at 90°, so 6² + t² = 10².