WAEC WAEC Nigeria General Mathematics
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Circle Theorems Applications
Circle Theorems Applications
Understanding Circle Theorems
Circle theorems are rules that help us understand the properties and relationships within circles. These theorems are useful for solving problems involving angles, triangles, and quadrilaterals in circles.
Key Circle Theorems
- Angle at the Centre Theorem: The angle subtended at the centre of a circle is twice the angle subtended at the circumference by the same arc.
- Angles in the Same Segment: Angles in the same segment of a circle are equal.
- Angle in a Semicircle: An angle subtended by a diameter at the circumference is a right angle (90°).
- Cyclic Quadrilateral Theorem: Opposite angles of a cyclic quadrilateral sum up to 180°.
- Tangent-Secant Theorem: The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
Applications of Circle Theorems
Circle theorems can be applied to solve various geometric problems. Here are some examples:
Worked Example
Example 1: Find the angle at the centre of a circle if the angle at the circumference is 35°.
Worked Example
Example 2: In a cyclic quadrilateral, if one angle is 110°, find the opposite angle.
Tuity Tip
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Visualize the Theorems: Drawing diagrams can help you see the relationships and apply the theorems more easily.
Check Your Work: Always verify your answers by checking if they satisfy the circle theorems.
Practice Makes Perfect: The more you practice, the better you'll understand and remember these theorems.
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