Let ABCD be a tangential quadrilateral and T_{1}, T_{2}, T_{3}, T_{4} be the tangency
points (see the figure below). Lines A_{1}C_{2}, A_{2}C_{1}, B_{1}D_{2}, B_{2}D_{1} are the common external tangent to the incircles of the triangles AT_{1}T_{4}, BT_{1}T_{2}, CT_{2}T_{3}, DT_{3}T_{4}. Prove that (1) lines A_{1}C_{2}, T_{1}T_{3}, and A_{2}C_{1} are parallel, similarly B_{1}D_{2}, T_{2}T_{4}, and B_{2}D_{1} are parallel, (2)
the quadrilateral E_{1}E_{2}E_{3}E_{4} is a
rhombus.

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Geometry Problems

Open Problems

Visual Index

Ten problems: 1411-1420

All Problems

Quadrilateral

Tangential or Circumscribed Quadrilateral

Incircle, Incenter, Inscribed circle

Circle

Circle Tangent Line

Triangle

Parallel lines

Parallelogram

Rhombus

Dynamic Geometry

GeoGebra

HTML5 and Dynamic Geometry

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