In the question below, our current GCSE students would be able to do part a, but not part b. Again, circle theorems feature heavily in the Geometry section of the 1974 O level exam. Interestingly the wording (but not the substance) of the circle theorems content on the 1974 O level Syllabus differs notably from the 1957 Syllabus. There was also a question in the 1957 paper relating to the Power of a Point Theorem, which now features in iGCSE (specifically the Intersecting Chords Theorem) but not GCSE. Our students might enjoy having a go at questions like this - the maths that their grandparents did at school. The question below is perhaps the easiest, and is similar in style to the questions seen on current GCSE papers. In the 1957 O level exam there were many questions relating to circle theorems, including a number of proofs. Note that the term 'cyclic quadrilateral' isn't used, but instead 'angles in opposite segments are supplementary'. Most of this looks very familiar, although the theorem 'if two circles touch, the point of contact is on the line of the centres' is not covered anymore. Looking back at the 1957 O level Syllabus, we have the following: Have circle theorems always featured on the UK curriculum? You only have to glance at an old textbook or O level paper to see that the topics studied at secondary school have changed considerably over the last century. What topics would you include? There's a lot of mathematics to choose from. Imagine designing a mathematics GCSE from scratch. In teaching this topic, we have the pleasure of exploring a set of theorems - a small selection of the many fascinating properties of circles - then teaching students how to apply their new mathematical knowledge to solve geometrical problems. They are the perfect example of a topic that is well placed in secondary school mathematics. There was no question about whether circle theorems should earn their place on the new mathematics curriculum.
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