Circle Geometry: The Theorems, With Examples — Worksheet & Memo

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Grade 11 · Euclidean Geometry

Circle Geometry: The Theorems, With Examples

MEMORANDUM

Name:

Class:

Date:

Mark

/ 15

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 AP̂B? (semicircle)
(1)
90° (angle in a semicircle)✓ (1)
4
In a semicircle, PÂB = 40°. Find AB̂P. (semicircle)
(2)
180° − 90° − 40° = 50°✓✓ (2)
5
Cyclic quad angle is 110°. Opposite angle? (cyclic quad)
(1)
180° − 110° = 70°✓ (1)
6
Cyclic quad angle is 75°. Opposite angle? (cyclic quad)
(1)
180° − 75° = 105°✓ (1)
7
Two angles stand on the same arc; one is 52°. The other? (same segment)
(1)
52° (equal)✓ (1)
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)
(1)
90° (tan ⊥ radius)✓ (1)
10
Angle at centre = 2x and equals 100°. Find x, the angle at the circumference. (solve)
(2)
2x = 100 → x = 50°✓✓ (2)

TOTAL: 15 marks