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2015a.00610 Hung, Tran Quang Two tangent circles from jigsawing quadrangle. Forum Geom. 14, 247-248 (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)