Grade 9 · Math · Unit 7 of 9
Circle Properties
Chords, tangents and angles
What your child practises
Using the rules of circle geometry: a perpendicular from the centre bisects a chord, a central angle is twice an inscribed angle on the same arc, inscribed angles on the same arc are equal, and a tangent meets the radius at 90°.
Nunavut Curriculum approved guide: Alberta Mathematics K–9 (2007), Shape and Space · 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
A circle has radius 5 cm. A chord is 8 cm long. How far is the chord from the centre, in cm?
answer boxcm
3 cm
Hint: The perpendicular from the centre meets the chord at its midpoint, 4 cm from each end. Use a right triangle with hypotenuse 5 and one leg 4: 5² − 4² = 9, and √9 = 3.
Question 2
A tangent touches a circle at T. O is the centre and P is a point on the tangent. Angle OPT is 24°. What is angle TOP, in degrees?
answer box°
66 °
Hint: A tangent is perpendicular to the radius at the point of contact, so angle OTP is 90°. The angles in triangle OTP add to 180°: 180 − 90 − 24 = 66.
Question 3
Two inscribed angles stand on the same arc. One measures 53°. How big is the other, in degrees?
answer box°
53 °
Hint: Inscribed angles on the same arc are equal.
Question 4
AB is a diameter of a circle of radius 4 cm. Point C is on the circle. What is angle ACB, in degrees?
answer box°
90 °
Hint: The diameter's central angle is 180°. The inscribed angle on the same arc is half of that: 90°.
Question 5
A line from the centre of a circle is perpendicular to a chord and meets it at M. The chord is 22 cm long. How long is the part from one end to M?
answer boxcm
11 cm
Hint: A perpendicular from the centre bisects the chord, so each half is 22 ÷ 2 = 11 cm.
Question 6
A central angle on an arc measures 92°. What is an inscribed angle on the same arc, in degrees?
answer box°
46 °
Hint: An inscribed angle is half the central angle: 92 ÷ 2 = 46.