Geometry Problem

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

Click the figure below to see the complete problem 666.

## Friday, September 9, 2011

### Problem 666: Intersecting Circles, Secant, Tangent, Concyclic points, Mind Map

Labels:
concyclic,
cyclic quadrilateral,
intersecting circles,
secant,
tangent

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angle CBD + angle CED

ReplyDelete= (angle CBA + angle ABC)+ angle CED

= angle ECD + angle EDC + angle CED (*)

= 180 degrees

=> E, C, B, D are concyclic

(*)angle between chord and tangent = angle in the

alternate segment

from previous problem, <ABE= <CDE-<ECD, and it is known that <ABD=<CDE, thus <EBD=<ECD and we are done.

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