Circle Theorems and Properties

This video tutorial covers seven circle theorems, focusing on their definitions and applications. It begins with an introduction to the parts of a circle, such as radius, diameter, and tangent. Theorems include the angle at the center being twice that at the circumference, angles in a semicircle containing a 90° angle, and opposite angles in a cyclic quadrilateral adding to 180°. The alternate segment theorem and properties of tangents are also discussed. The video is designed for students transitioning from foundation to higher level in AQA unit 3.

What is the term for the distance around a circle?

• Circumference

• Radius

• Diameter

• Perimeter

Which part of a circle is a line segment that does not pass through the center?

• Tangent

• Diameter

• Radius

• Chord

What is the name of the part of a circle that looks like a slice of cake?

• Chord

• Segment

• Sector

• Arc

According to the first circle theorem, the angle at the center of a circle is how many times the angle at the circumference?

• Thrice

• Half

• Equal

• Twice

In a semicircle, what is the measure of the angle at the circumference?

• 90°

• 180°

• 60°

• 45°

If two angles are drawn from the same arc to the circumference, what can be said about these angles?

• They are complementary

• One is double the other

• They are equal

• They are supplementary

What is the sum of the opposite angles in a cyclic quadrilateral?

• 180°

• 360°

• 90°

• 270°

What is the alternate segment theorem about?

• Angles in a semicircle

• Angles from the same arc

• Angles in a cyclic quadrilateral

• Angles between a tangent and a chord

When a tangent meets a radius, what is the angle formed?

• 90°

• 60°

• 120°

• 45°

If two tangents are drawn from the same point to a circle, what can be said about their lengths?

• They are equal

• One is double the other

• They are complementary

• They are supplementary