
06349709
j
2015a.00610
Hung, Tran Quang
Two tangent circles from jigsawing quadrangle.
Forum Geom. 14, 247248 (2014).
2014
Florida Atlantic University, Department of Mathematical Sciences, Boca Raton, FL
EN
G45
tangent circles
jigsawing a quadrangle
http://forumgeom.fau.edu/FG2014volume14/FG201425index.html
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 $TB=TC$.
Antonio M. Oller (Zaragoza)