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Geometry ProblemPost your solution in the comment box belowLevel: Mathematics Education, High School, Honors Geometry, College.Click the figure below to see the complete problem 915.
Join D to F and extend it to D1. ///ly join G to F and extend to G1. Since ADFE is concyclic, /_EFD1 =/_A. ///ly /_GFD1=/B which implies that /_EFG1=/_C since A,B & C are internal angles of Tr. ABC. This, in turn, means that quad CEFG is concyclic.
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angle(EFG) = 360 - angle(DFE) - angle(DFG)= (180- angle(DFE)) + (180 - angle(DFG))= A + B= 180 - C= 180 - angle(GCE)q.e.d.
∠A + ∠DFE = 180°∠B + ∠DFG = 180°∠C + ∠EFG= (180°−∠A−∠B) + (360°−∠DFE−∠DFG)= 540° − (∠A + ∠DFE) − (∠B + ∠DFG)= 180°Thus, C,E,F,G concyclic.
Antonio,I would like to propose a new problem:D is located inside the triangle ABC, such that <DAC=<DAB=<DBA=10 degrees.<DBC is 30 degrees. Find <ACD.Respectfully,Erina-NJ