8. The Four Concurrency Theorems
diag11 applet
Drag the vertices of the triangles. Remember, the convention is that red points are dragable ...

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diag12 applet
For authors: Gemeter's Bisect Angle cannot be converted to Java, but I have used a nice workaround ...

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diag13 applet

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diag14 applet

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diag8 & 9-applets
  1. Two circles touch only at one point. Investigate the relationship formed between the common tangents and the chords that meet these tangents. Can you generalise your findings?
    Click on the red points in the circles below, and while holding down the mouse button, drag the points to change the sizes of the circles.

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diag10 applet
  1. What if three circles touch? Can you generalise your previous results?
    Also investigate the ratio of the length of the sides of the triangles in the diagram.
  2. Can you explain or prove your findings?
Click on the red points in the circles below, and while holding down the mouse button, drag the points to change the sizes of the circles.

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diag16 pic
Orthocentre

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