This document outlines 8 circle theorems: 1) The angle at the center is twice the angle at the circumference. 2) The angle in a semi-circle is 90 degrees. 3) Angles in the same segment are equal. 4) Opposite angles in a cyclic quadrilateral add up to 180 degrees. 5) The lengths of the two tangents from a point to a circle are equal. 6) The angle between a tangent and a radius in a circle is 90 degrees. 7) The angle between the tangent and chord at the point of contact equals the angle in the alternate segment. 8) A perpendicular from the center bisects a chord.

1. Circle Theorem
Basic facts on circle
The Circle
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2. Circle Theorem 1
The angle at the center is twice the
angle at the circumference.

3. Circle Theorem 2
The angle in a semi-cicle is 90°.

4. Circle Theorem 3
Angles in the same segment
are equal.

5. Circle Theorem 4
Opposite angles in a cyclic
quadrilateral add up to 180°.

6. Circle Theorem 5
The lengths of the two tangents
from a point to a circle are equal.

7. Circle Theorem 6
The angle between a tangent and
a radius in a circle is 90°.
.

8. Circle Theorem 7
Alternate segment theorem:
The angle (α) between the tangent and the
chord at the point of contact (D) is equal to the
angle (β) in the alternate segment*.
.

9. Circle Theorem 8
Perpendicular from the centre bisects
the chord: