From-a-point-on-the-circumcircle-of-an-equilateral-triangle-ABC-parallels-to-the-sides-BC-CA-and-AB-are-drawn-intersecting-the-sides-CA-AB-and-BC-at-the-points-M-N-P-respectively-Prove-that-the

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Question Number 16877 by Tinkutara last updated on 27/Jun/17

From a point on the circumcircle of an equilateral triangle ABC parallels to the sides BC, CA and AB are drawn, intersecting the sides CA, AB and BC at the points M, N, P, respectively. Prove that the points M, N and P are collinear.

$$\mathrm{From}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{circumcircle}\:\mathrm{of}\:\mathrm{an} \\ $$$$\mathrm{equilateral}\:\mathrm{triangle}\:{ABC}\:\mathrm{parallels}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{sides}\:{BC},\:{CA}\:\mathrm{and}\:{AB}\:\mathrm{are}\:\mathrm{drawn}, \\ $$$$\mathrm{intersecting}\:\mathrm{the}\:\mathrm{sides}\:{CA},\:{AB}\:\mathrm{and}\:{BC} \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{points}\:{M},\:{N},\:{P},\:\mathrm{respectively}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{points}\:{M},\:{N}\:\mathrm{and}\:{P}\:\mathrm{are} \\ $$$$\mathrm{collinear}. \\ $$

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From-a-point-on-the-circumcircle-of-an-equilateral-triangle-ABC-parallels-to-the-sides-BC-CA-and-AB-are-drawn-intersecting-the-sides-CA-AB-and-BC-at-the-points-M-N-P-respectively-Prove-that-the

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