Dynamic Geometry Problem 1470: Tangential Quadrilateral, Incircles, Tangent, Parallel, Rhombus.

Let ABCD be a tangential quadrilateral and T1, T2, T3, T4 be the tangency points (see the figure below). Lines A1C2, A2C1, B1D2, B2D1 are the common external tangent to the incircles of the triangles AT1T4, BT1T2, CT2T3, DT3T4. Prove that (1) lines A1C2, T1T3, and A2C1 are parallel, similarly B1D2, T2T4, and B2D1 are parallel, (2) the quadrilateral E1E2E3E4 is a rhombus.

See solution below

Static Diagram of Geometry Problem 1470

Poster of Problem 1465, Tangential Quadrilateral, Incenter, Inscribed Circle, Step-by-step Illustration, GeoGebra, iPad

See solution below

Poster of Geometry Problem 1470 using iPad Apps

Poster of Problem 1470, Tangential Quadrilateral, Incircles, Tangent, Parallel, Rhombus, Step-by-step Illustration, GeoGebra, iPad

Search gogeometry.com

Classroom Resource:
Interactive step-by-step animation using GeoGebra

This step-by-step interactive illustration was created with GeoGebra.

  • To explore (show / hide): click/tap a check box.
  • To stop/play the animation: click/tap the icon in the lower left corner.
  • To go to first step: click/tap the "Go to step 1" button.
  • To manipulate the interactive figure: click/tap and drag the blue points or figures.

GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus application, intended for teachers and students. Many parts of GeoGebra have been ported to HTML5.

Recent Additions

Geometry Problems
Open Problems
Visual Index
Ten problems: 1411-1420
All Problems
Tangential or Circumscribed Quadrilateral
Incircle, Incenter, Inscribed circle
Circle Tangent Line
Parallel lines
Dynamic Geometry
HTML5 and Dynamic Geometry
iPad Apps
View or Post a solution

Geometry Problem 1470 Solution(s)