The diagram below shows a red unit circle with a dynamic blue circle intersecting it at (0, -1) and (0, 1). The measures of the x-coordinates of the dynamic blue circle intersecting the x-axis at points B and B' are shown.
Investigate & Conjecture
1) Drag the point OB. What do you notice regarding the x-coordinates of B and B'?
2) What do you notice about the path of H, the highest point of the blue circle? Can you find a formula for the curve?
Intersecting Circles
Check your conjectures
3) Check your conjectures by clicking on the red buttons on the bottom right of the screen.
Challenge
4) Can you logically explain (prove) your conjectures above?
Reference
A paper Intersecting Circles Investigation (761 KB) related to the above, by James Metz, Brad Uy & myself, has been published in the journal At Right Angles (12.9 MB), Nov 2022, pp. 67-73.
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Created by Michael de Villiers, 13 July 2021 with WebSketchpad; updated 17-18 August; 22 November 2022.