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Answer to Question #48607 in Trigonometry for Mr. X

Question #48607
Prove the following extension of Moreley's theorem.
Consider ∆ABC.
Let adjacent trisectors of external angles B and C meet at P.
Let adjacent trisectors of external angles C and A meet at Q.
Let adjacent trisectors of external angles A and B meet at R.
Prove that ∆PQR is equilateral.
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