Invent geometry tasks that require a proof
The properties detected with OK Geometry can be a rich source of proving tasks in planar geometry.
Observing even a simple configuration with OK Geometry brings to light many of its properties. Some of them may be trivial or irrelevant for some reason, but we can often find among them interesting, non-trivial and perhaps unexpected properties that can serve as proving task.
Here is an example. Consider the following configuration, which we use also as the first part of the proving tasks:
Let O be the circumcentre of a given triangle ABC and let D be the intersection of lines CO and AB. Finally, let E and F be the orthogonal projections of D onto the sidelines AC and BC respectively.
The observation of this configuration with OK Geometry generates a long list of properties. We selected some of the properties and shape each of them as an instruction to be individually added to the task setting:
 
Prove that the triangles ADE and DFC are similar.
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Prove that the line EF is parallel to the baseline AB.
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Prove that the area of triangle ADC is twice the area of triangle EOC.
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 Prove that the points D, F, C, E lay on the same circle. |
 Prove that the line DE is tangent to the circle through points B, C, D. |
 Prove that the circle through A,E,F, the circle through D,O,F, and the line through A,O meet in a common point. |