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Geometry Education Proposed Problem 352 |
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Problem 352. Tangential quadrilateral, Incircles, Common tangent,
Circumscribable or Tangential quadrilateral.
The figure shows a tangential
quadrilateral ABCD
with a point E on side BC. Circles 1 and 2 are the incircles
of triangles ABE and CDE, respectively. FG is the common
tangent to circles 1 and 2. FG intersects to AE and DE at M and
N, respectively. Prove that the
quadrilateral AMND is circumscribable or tangential (sides all lie tangent to a single circle inscribed within the quadrilateral). Post
a
comment.
Geometry problem solving
Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given." |
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