Triangle with Hexagon and Equilateral Triangle on Two Sides

Hint 1: Use a GSP construction and move point A to various positions. Note that A will not always be located on the same side of segment PQ.

Hint 2: You will probably need some auxiliary constructions. Try rotating the figure about R.

We need a figure which guarantees a right angle. For example, can we show P, Q, and R are points on a circle with PQ as a diameter?

Another example, can we develop a figure where the two segmes PR and RQ must be perpendicular?GSP file (or construct your own).

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