Ohne Titel

Circle Theorems

• Circle theorems are a set of theorems that can be used to find the length of lines or the sizes of an angle in a circle, similar to many of the rules that govern triangles. There are 6 theorems that you need to learn for GCSE maths.

Circle Theorems

• Circle theorems are similar to many of the rules that govern triangles, they too can be used to find the length and size of angles and lines. There are 6 theorems that are needed to learn for GCSE maths.
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segments, Sectors, chords, tangents

• This is the basic terminology needed for understanding circle theorems.
• CHORD; A chord is any straight line going from on edge of the circle to another.
• SEGMENT; A segment is simply a segment, it is part of a circle sectioned away with a chord.
• SECTOR; A proportion of sectioned away with lines from the centre of the circle. ie. A slice of pizza, is a sector of a circle.
• ARCS; An arc is part of the circumference separated with a sector
• Tangent; A straight line, outside of the circle just touching the circumference at one spot.
• On to the theorems!
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THEOREM ONE; Angles in a semi circle 90

• This theorem states; Angles in a semi circle are 90 degrees. This means; A triangle drawn from the two ends of the diameter will always make an angle of 90 degrees when it meets the edge of the circle. This is a bit difficult to visualise so heres a easier description;
• Look at the diameter, if the diameter forms the base of a triangle, and the tip of the triangle touches the circumference then the angle at the circumference is 90 degrees. ( Hope thats easier to understand )
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TWO; Angles in same seg.* are equal

• This theorem states, angles in the same segment are equal, which means; All triangles drawn from a chord will have the same angle where they touch the circle. Also, the two angles on opposite sides of the chord add up to 180 degrees.
• I'll try to describe it more visually; If you have a chord ( so just a straight line across the circle ) and the chord forms the base of two triangles that are both formed the same side of the chord, then both the angles at the circumference are equal, lets call these triangle's 'y'.
• Then if you form two more triangles ON THE OTHER SIDE of the chord ( lets call these triangles 'x' ) then the angles at the circumference of x and y will add up to 180 degrees.
• Seg= Segment