What are the 8 circle theorems?

What are the 8 circle theorems?

• Circle Theorem 1 – Angle at the Centre.
• Circle Theorem 2 – Angles in a Semicircle.
• Circle Theorem 3 – Angles in the Same Segment.
• Circle Theorem 4 – Cyclic Quadrilateral.
• Circle Theorem 5 – Radius to a Tangent.
• Circle Theorem 6 – Tangents from a Point to a Circle.
• Circle Theorem 7 – Tangents from a Point to a Circle II.

How do I learn circle theorems?

Circle theorems: where do they come from?

1. The angle at the centre is twice the angle at the circumference.
2. The angle in a semicircle is a right angle.
3. Angles in the same segment are equal.
4. Opposite angles in a cyclic quadrilateral sum to 180°
5. The angle between the chord and the tangent is equal to the angle in the alternate segment.

What is the rule of circle?

A circle is all points in the same plane that lie at an equal distance from a center point. The circle is only composed of the points on the border. A circle is the same as 360°. You can divide a circle into smaller portions. A part of a circle is called an arc and an arc is named according to its angle.

What are the six circle theorems?

In geometry, the six circles theorem relates to a chain of six circles together with a triangle, such that each circle is tangent to two sides of the triangle and also to the preceding circle in the chain.

Why are inscribed angles half the arc?

Proof: The measure of each inscribed angle is exactly half the measure of its intercepted arc. Since they have the same intercepted arc, they have the same measure. Proof: The intercepted arc for an angle inscribed in a semi-circle is 180 degrees. Therefore the measure of the angle must be half of 180, or 90 degrees.

Can two inscribed angles intercept the same arc?

Theorem 71: If two inscribed angles of a circle intercept the same arc or arcs of equal measure, then the inscribed angles have equal measure.