@article {MATHEDUC.06349709,
author = {Hung, Tran Quang},
title = {Two tangent circles from jigsawing quadrangle.},
year = {2014},
journal = {Forum Geometricorum},
volume = {14},
issn = {1534-1178},
pages = {247-248},
publisher = {Florida Atlantic University, Department of Mathematical Sciences, Boca Raton, FL},
abstract = {Let $ABC$ be an acute angled triangle. Van Lamoen has given the following construction: $P$ and $Q$ are a pair of isotomic points lying on $BC$, the perpendicular to $BC$ through $P$ intersects $AB$ at $P'$, the perpendicular to $BC$ through $Q$ intersects $AC$ at $Q'$, if we rotate $BPP'$ and $CQQ'$ about $P'$ and $Q'$ so that $P$ and $Q$ overlap, then also $B$ and $C$ overlap at a point $A'$. The quadrangle $AP'A'Q'$ is cyclic. If $S$ is the circumcenter of $AP'A'Q'$ and $T$ is the intersection of the tangents at $B$ and $C$ to the circumcircle of $ABC$ this paper proves that the circumcircle of $AP'A'Q'$ is tangent at $A'$ to the circle of center $T$ and radius $TB=TC$.},
reviewer = {Antonio M. Oller (Zaragoza)},
msc2010 = {G45xx},
identifier = {2015a.00610},
}