Circle Theorems

Circle Theorems

The theorems are rules that helps us calculate the measures of angles or line segments.

Expectation:

By the end of this lesson, you will be able to solve problems using circle theorems

Theorem 1: Angles in the same segment are equal

Angles subtended at the circumference by a chord or arc in the same segment of a circle are equal.

Example 1: 

In the diagram below PQ is a chord, PQRS are points on the given circle. Find the value of x .

Example 2:

The diagram below is a circle with chord AB subtending angles AEB, ADB, and ACB at the circumference. Find the value of m + n. 

Try:

The diagram below is a circle with chord AB subtending angles AEB, ADB, and ACB at the circumference.
Find the value of i) <BDA     ii) m

Theorem 2:

The angle subtended at the centre of a circle is double that subtended at the circumference.

Example 3

In the diagram, WXY is a circle with centre O, angle XOY=110 degrees. Find the value of angle XWY.






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