Hi Golland,

This deltoid problem, like Dracula, keeps coming back from the dead.

The following figure shows the deltoid for an equilateral triangle ABC ( not really - the arcs are circular ). Where G is the centroid and X* is the midpoint of the median through vertex X.

http://geocities.com/bractals/Eq-delt.gif

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My final conjecture (until next week - haha) about the number of line solutions for a point:

3 - The centroid G and the interior of the "triangles" A*B*G, B*C*G, and C*A*G
2 - Arcs A*B*, B*C*, and C*A* excluding the endpoints
1 - All other points
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See if you can find 3 solution lines for any point on the open line segment (A*G).

As for your two problems, let me think about them.

With respect to the area problem, would you agree that solving the problem for an equilateral triangle is enough?

Will be gone for a week.

Bractals