Let ABCDE be a convex pentagon such that AB = BC = CD and angle BDE =
angle EAC = 30. Find the possible values of angle BEC.
Circle B contains A and C. Let C' be the 30 degree rotation of C. Let E' be the intersection of circle B and ray BC'. E'BC=60 degrees and BC=BE'
Similarly circle C contains B and D. Let B' be the -30 degree rotation of B. Let E" be the intersection of circle C and ray DB'. E"CB=60 degrees and BC=CE"
Thus E'=E"=E and triangle BCE is equilateral. Angle BEC must be 60 degrees
https://www.geogebra.org/geometry/dkv5jsvv
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Posted by Jer
on 2024-04-14 12:52:43 |
Solution
