I appreciate that you won’t know for certain, but in your opinion how many marks would I get if I correctly came to an expression but in terms of ‘a’, ‘b’ and ‘r’ rather than only ‘a’ and ‘b’?
I don’t think you’d get many marks for that. The hard bit is getting the area of the circle in terms of a and b, which is what you need to do to eliminate r from the answer. So my guess at the mark would be no more than 2/6; if I were doing a mark scheme I would most likely give it 1/6.
Can you label the triangle and tell me which are the two triangles that are similar
It will be a few days before I can scan anything in so in the meantime I will try to describe the diagram in more detail.
Look at the big right angled triangle that I have drawn (this represents one of the quarters of the rhombus). The radius of the circle touches the hypotenuse of the triangle and makes a right angle with it (because it is the tangent to the circle drawn in the question). This line splits the big triangle up into two: one small one at the bottom and a tiny one at the top. The tiny triangle shares an angle with the big one (top right), and they both also have a right angle, therefore all three of their angles are the same, and so they are similar.
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