# What are the six circle theorems?

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science
space and astronomy

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. The chain closes, in the sense that the sixth**circle**is always tangent to the first**circle**.

Herein, what are the 7 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.

**angles**at the centre and at the circumference. Second circle theorem -

**angle**in a semicircle. Third circle theorem -

**angles**in the same segment. Fourth circle theorem -

**angles**in a cyclic quadlateral.

Regarding this, how many circle theorems are there?

8 circle theorems

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