MATHS - Geometry - Circle Theorems Part 1

This video tutorial introduces four circle theorems, each explained with examples. The first theorem states that the angle at the center of a circle is double the angle at the circumference. The second theorem explains that the angle in a semicircle is always 90 degrees. The third theorem describes that angles in the same segment are equal, and the fourth theorem covers cyclic quadrilaterals, where opposite angles sum to 180 degrees. The video concludes with a review and practice questions to reinforce learning.

What is the relationship between the angle at the center and the angle at the circumference of a circle?

• The angle at the center is triple the angle at the circumference.

• The angle at the center is equal to the angle at the circumference.

• The angle at the center is double the angle at the circumference.

• The angle at the center is half the angle at the circumference.

What is the measure of the angle in a semicircle?

• 120 degrees

• 90 degrees

• 60 degrees

• 45 degrees

How can angles in the same segment of a circle be described?

• They are supplementary.

• They are complementary.

• They are equal.

• They are always different.

What is a cyclic quadrilateral?

• A quadrilateral with all angles equal.

• A quadrilateral with all sides equal.

• A quadrilateral with opposite sides parallel.

• A quadrilateral with all vertices touching the circumference of a circle.

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

• 360 degrees

• 270 degrees

• 180 degrees

• 90 degrees