id: 06349709
dt: j
an: 2015a.00610
au: Hung, Tran Quang
ti: Two tangent circles from jigsawing quadrangle.
so: Forum Geom. 14, 247-248 (2014).
py: 2014
pu: Florida Atlantic University, Department of Mathematical Sciences, Boca
Raton, FL
la: EN
cc: G45
ut: tangent circles; jigsawing a quadrangle
ci:
li: http://forumgeom.fau.edu/FG2014volume14/FG201425index.html
ab: 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 $TB=TC$.
rv: Antonio M. Oller (Zaragoza)