Circle theorems - Part 2

Circle Theorems - Part 2

Alternate Segment Theorem

• The alternate segment theorem states that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
• This means that the angle subtended by the chord at the edge of the circle is the same as the angle between the chord and the tangent.

Angles in the Same Segment Theorem

• The theorem which deals with angles in the same segment states that angles subtended by the same arc (or chord) are equal.
• This applies no matter where the two angles are located on the circumference, as long as they are on the same side of the line from the circle’s centre to the middle of the arc.

Angle at the Centre Theorem

• The angle at the centre theorem claims that the angle subtended by an arc at the centre of a circle is twice the angle subtended by it at any point on the alternate segment.
• This is true, regardless of the size of the arc or its placement inside the circle.

Cyclic Quadrilateral Theorem

• The cyclic quadrilateral theorem states that the opposite angles of a quadrilateral that can be inscribed in a circle (a cyclic quadrilateral) add up to 180 degrees.
• For any four-sided shape that can be drawn inside a circle so that each of its corners touches the circumference, this theorem can be applied.

Remember, being aware of circle theorems and their application is crucial for tackling geometry problems. These theorems offer a systematic approach for working with circles and related geometric shapes. Practice these theorems using a variety of problem sets to cement your understanding.