Euclidean Geometry is one of 9 topics in the Grade 11 Technical Mathematics CAPS syllabus, covered across 3 lessons on Study Vault. Below are real practice questions from this topic with full worked answers.
Sample practice questions
Easy
1. A line is drawn from the centre of a circle perpendicular to a chord. What does this theorem tell us the line does to the chord?
Bisects the chord (cuts it into two equal halves)
Makes the chord twice as long
Has no effect on the chord
Always passes outside the circle
Answer: Bisects the chord (cuts it into two equal halves) — The line from the centre perpendicular to a chord always bisects that chord.
Easy
2. According to the inscribed angle theorem, how does the angle at the centre compare to the angle at the circumference (subtended by the same arc)?
The angle at the centre is double the angle at the circumference
The angle at the centre equals the angle at the circumference
The angle at the centre is half the angle at the circumference
There is no fixed relationship
Answer: The angle at the centre is double the angle at the circumference — The angle subtended by an arc at the centre is always double the angle subtended by the same arc at the circumference (on the same side of the chord).
Medium
3. A circle has radius 13cm. A chord is 5cm from the centre, measured perpendicular to the chord. Find half the length of the chord, in cm.
Answer: 12 — The perpendicular from the centre bisects the chord, forming a right-angled triangle with the radius as hypotenuse: half-chord = sqrt(13^2-5^2) = sqrt(169-25) = sqrt(144) = 12cm.
