Advanced Euclidean Geometry
Advanced Euclidean Geometry
Advanced Euclidean Geometry
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Pf: A<br />
C<br />
Miquel Point<br />
E G<br />
J<br />
H<br />
F<br />
D<br />
I<br />
B<br />
In circle J,<br />
∠EGD + ∠C = π.<br />
In circle I,<br />
∠FGD + ∠B = π.<br />
Since ∠EGF + ∠FGD + ∠EGD + ∠A + ∠B + ∠C = 2π + π, by<br />
subtracting we get ∠EGF + ∠A = π and so A,E,G and F are<br />
concyclic (on the same circle).