Given three points P,Q and R, how May I find another point O such that OP,OQ and OR are all perpendicular between themselves? I have no idea how to tackle this
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1you know about the theorem of Thales, https://en.wikipedia.org/wiki/Thales%27s_theorem? – Thomas Dec 02 '21 at 15:16
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Are you aware of orthocenter? – nonuser Dec 02 '21 at 15:22
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How is your reasoning when you say "May I find another point $O$ " Another one, but what is the first $O$ ??? You don't mention it. Usually $O$ is used for the circumcenter of a triangle. – Jean Marie Dec 02 '21 at 15:39
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Yes Aqua, I know the orthocenter. – user10000024 Dec 02 '21 at 15:41
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First of all, decide if it's a 2d problem or a 3d problem. – MyMolecules Dec 02 '21 at 15:46
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It's a 3d problem – user10000024 Dec 02 '21 at 15:47
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Ok, so next try to find relation/position of O wrt P, Q, R. Add your attempts to the post. – MyMolecules Dec 02 '21 at 15:56
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HINT. Point $O$ must lay on the sphere of diameter $PQ$... etc. – Intelligenti pauca Dec 03 '21 at 22:21