Let-P-be-a-point-on-the-circumcircle-of-the-equilateral-triangle-ABC-Prove-that-the-projections-of-any-point-Q-onto-the-lines-PA-PB-and-PC-are-the-vertices-of-an-equilateral-triangle-

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Question Number 16878 by Tinkutara last updated on 27/Jun/17

Let P be a point on the circumcircle of the equilateral triangle ABC. Prove that the projections of any point Q onto the lines PA, PB and PC are the vertices of an equilateral triangle.

$$\mathrm{Let}\:{P}\:\mathrm{be}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{circumcircle}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{equilateral}\:\mathrm{triangle}\:{ABC}.\:\mathrm{Prove} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{projections}\:\mathrm{of}\:\mathrm{any}\:\mathrm{point}\:{Q} \\ $$$$\mathrm{onto}\:\mathrm{the}\:\mathrm{lines}\:{PA},\:{PB}\:\mathrm{and}\:{PC}\:\mathrm{are}\:\mathrm{the} \\ $$$$\mathrm{vertices}\:\mathrm{of}\:\mathrm{an}\:\mathrm{equilateral}\:\mathrm{triangle}. \\ $$

Commented by prakash jain last updated on 28/Jun/17

$$\mathrm{P}=\mathrm{A}? \\ $$

Commented by prakash jain last updated on 28/Jun/17

$${what}\:{jappens}\:{when}\:{P}={A} \\ $$

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