Geometry Problem. GeoGebra, HTML5 Animation for iPad and Nexus.

Post your solution in the comments box below.

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the dynamic geometry demonstration of problem 899.

## Tuesday, July 9, 2013

### Problem 899: Intersecting Circles, Common External Tangent, Secant, Concyclic Points, Cyclic Quadrilateral

Labels:
common tangent,
concyclic,
GeoGebra,
HTML5,
intersecting circles,
ipad

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∠FBD

ReplyDelete= ∠FBA + ∠ABD

= (180-∠FCA) + ∠AED

= 180-(∠CGD + ∠AED) + ∠AED

= 180 - ∠CGD

= 180 - ∠FGD

So F,B,G,D are concylic,

symmetrically, B,G,C,E are concylic.

Angle BED=angle FAB=angle FCB=180-angle GCB. Hence GCBE is cyclic. Similarly, angle BFG=angle BAE=angle BDE=180-angle BDG. Hence, BFGD is cyclic.

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