Geometry Problem 1351: Two Tangential or Circumscribed Quadrilaterals, Midpoints, Perpendiculars. Math, Tutoring.

Proposition

The figure below shows a tangential or circumscribed quadrilateral ABCD. A1, B1, C1, and D1 are the midpoints of AB, BC, CD, and AD, respectively. A1A2, B1B2, C1C2, and D1D2 are perpendicular to CD, AD, AB, and BC, respectively. A1A2 cuts B1B2 at A3, B1B2 cuts C1C2 at B3, C1C2 cuts D1D2 at C3, and D1D2 cuts A1A2 at D3. Prove that A3B3C3D3 is a tangential quadrilateral.


Geometry Problem 1351: Two Tangential or Circumscribed Quadrilaterals, Midpoints, Perpendiculars. Math Infographic, Tutor


See also:
Art of Problem 1351 using iPad Pro Apps.