Circles

Question 1

What is the equation for the area of a circle?

Answer 1

πr²
π x radius²

Question 2

What is the equation for the circumference of a circle?

Answer 2

πd OR π2r
π x diameter OR π x 2 x radius

Question 3

What are the eight circle terms?

Answer 3

• Arc
• Sector
• Circumference
• Segment
• Chord
• Radius
• Diameter
• Tangent

Question 4

How do you prove that the angle in a semicircle is a right angle? (Circle Theorem 1)

Answer 4

Question 5

How do you prove that the angle at the center of a circle is double the angle at the circumference? (Circle Theorem 2)

Answer 5

Question 6

How do you prove that the angles in the same segment are equal? (Circle Theorem 3)

Answer 6

Question 7

How do you prove that the angles in a cyclic quadrilateral add up to 180°? (Circle Theorem 4)

Answer 7

Question 8

How do you prove that a tangent is perpendicular to a radius? (Circle Theorem 5)

Answer 8

Question 9

How do you prove that the tangents from a point are equal? (Circle Theorem 6)

Answer 9

They have the same length for r and share x and the 90° angle, so are similar shapes.

Question 10

How do you prove that the angles in alternate segments are equal? (Circle Theorem 7)

Answer 10