Circle Theorems - GCSE Higher Maths
1st Class Maths・2 minutes read
Circle theorems explain how different angles and segments interact within a circle, such as equal angles in the same segment, right angles with a diameter, and the relationship between central and circumferential angles. By understanding these theorems, one can solve geometry problems involving circles by identifying angles and applying the theorems to determine missing angles accurately.
Insights
- A chord in a circle divides it into two sections, with angles in the same section being equal, even if the chord is absent.
- The application of circle theorems in problem-solving revolves around recognizing angles and utilizing the theorems to uncover missing angles, offering a systematic approach to geometric challenges.
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Recent questions
What happens when a chord is drawn in a circle?
It splits the circle into two segments with equal angles.
What is the relationship between the angle at the center and the circumference of a circle?
The angle at the center is twice the angle at the circumference.
What is the significance of a tangent meeting a radius in a circle?
It forms a 90-degree angle.
How are angles related in a cyclic quadrilateral?
Opposite angles add up to 180 degrees.
What happens when a line is drawn from the center of a circle to a point on the circle?
It bisects the angle at that point.
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Summary
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Circle Theorems: Angles, Chords, and Tangents
- A chord in a circle splits it into two segments, with angles in the same segment being equal.
- The angles in the same segment are equal, regardless of the presence of the chord.
- If a chord is a diameter, the angles created are always right angles.
- The angle at the center of a circle is twice the angle at the circumference.
- A cyclic quadrilateral has opposite angles that add up to 180 degrees.
- A tangent meeting a radius forms a 90-degree angle.
- Tangents from the same point to a circle are equal in length.
- A line from the center of a circle to a point on the circle bisects the angle at that point.
- The angle the tangent makes with a chord is equal to the angle the chord makes at the circumference.
- Applying circle theorems to solve problems involves identifying angles and using the theorems to find missing angles.
