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Circle Geometry

Drawing of a circle showing the angle subtended at the centre by an arc and two angles subtended at different places on the circumference by the same arcAs a child, I remember being mystified how a circle could hold any great secrets. After all circles are so easy to construct and they look the same from all directions.

How wrong I was!

In studying circles, as with investigating anything of importance, one question leads to another, and insights gained in other areas of mathematics prove to be relevant to our study and reveal yet more hidden patterns. Entire books have been written about the geometry of circles, and even more books about π, the ratio between a circle’s circumference (perimeter) and diameter.

I remember being astounded when I learned that the size of the angle at the centre of a circle (the yellow angle in this image) is always exactly twice the size of ANY blue angle on the circumference!  The ratio was always two, and the conclusion was that it did not matter where on the circumference you placed the angle, it would always be the same size … if it was standing on the same arc.  Such amazing simplicity!  And so, my adventure with circles began.

As you will see, there is so very much more to discover …


We were all deeply impressed with Graeme from the very beginning. [Lucas’] confidence radically changed within only 3 weeks of Graeme’s instruction and assistance. I am sure this was largely attributed to Graeme’s infectious passion and love for his subject, and his high personal level of skill, teaching experience and understanding of mathematics. Lucas always found Graeme could explain concepts so knowledgeably and easily, which really did transform Lucas’ appreciation and enjoyment of the subject. Graeme always gave Lucas assistance and time over and above his hour’s tutoring session. Graeme has developed a wonderful relationship and more of a mentoring role which has been of great assistance and value to Lucas as he faces the pressures of his final year of school.  I have no hesitation in recommending Graeme as an outstanding tutor and friend, and a very wise, knowledgeable and capable teacher of the highest calibre.
Sally T (parent, 2005)

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