Online Geometry theorems, problems, solutions, and related topics.
Geometry Problem. Post your solution in the comments box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the figure below to enlarge the problem 939.
<EDC=<ECA (tangent angle theorem) and <EDC=<EAF (parallel). That makes circumcircle of EAC tangent to FA and then by powerpoint theorem, FA^2=FE*FC. But FB^2=FE*FC, so FB^2=FA^2
Construct circle circumscribe AECAngleBAE=angleEDC=angleECASo AB is tangent to circle O and also to new constructed circle.Further as FEC is the common chord of both circles it will bisect the tangent segment QED