## Intersecting Circles Investigation

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?

#### .sketch_canvas { border: medium solid lightgray; display: inline-block; } Intersecting Circles

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.