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Orthocenter and Altitude Construction Puzzles

Segment AD is an altitude of triangle ABC. Construct the most "flexible" triangle ABC possible.

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Segment AD is an altitude of triangle ABC and line BH contains the altitude from B to side AC. Construct the most "flexible" triangle ABC possible.

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Given orthocenter H and side AB, construct the most "flexible" triangle ABC possible.

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Given orthocenter H and triangle vertex A, construct the most "flexible" triangle ABC possible.