Circle Geometry: Every Theorem, With Examples — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 11 · Euclidean Geometry

Circle Geometry: Every Theorem, With Examples

MEMORANDUM

Name:

Class:

Date:

Mark

/ 20

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Arc subtends 120° at the centre. Angle at the circumference? (centre/circ)
(2)
120 ÷ 2 = 60°✓✓ (2)
2
Angle at the circumference is 35°. Angle at the centre (same arc)? (centre/circ)
(2)
2 × 35 = 70°✓✓ (2)
3
AB is a diameter, P on the circle. What is ∠APB? (semicircle)
(2)
90° (angle in a semicircle)✓✓ (2)
4
In a semicircle, ∠PAB = 40°. Find ∠ABP. (semicircle)
(2)
180 − 90 − 40 = 50°✓✓ (2)
5
Cyclic quad angle is 110°. Opposite angle? (cyclic quad)
(2)
180 − 110 = 70°✓✓ (2)
6
Cyclic quad angle is 75°. Opposite angle? (cyclic quad)
(2)
180 − 75 = 105°✓✓ (2)
7
Two angles stand on the same arc; one is 52°. The other? (same segment)
(2)
52° (equal)✓✓ (2)
8
Tangent–chord angle is 70°. Angle in the alternate segment? (tan–chord)
(2)
70°✓✓ (2)
9
A tangent meets a radius at the point of contact. What is the angle? (tan–radius)
(2)
90° (tan ⊥ radius)✓✓ (2)
10
Angle at centre = 2x and equals 100°. Find x, the angle at the circumference. (solve)
(2)
2x = 100 → x = 50°✓✓ (2)

TOTAL: 20 marks