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 938.
Conjecture: O₁OO₂E form a parallelogram. If so, then using parallelogram law, EO² + 9² = 2(4² + 6²)EO = √23Unfortunately, I still need some time to prove / disprove my assertion.
Let <BAE=a and <EBA=b. Then <OO1E=1/2<BO1A-<BO1E=(a+b)-2a=b-a. From cyclic condition we find that <EO2O=1/2<CO2D-<CO2E=b-a as well. If AB and CD meet at point P, <DPB=<DCA-<BAE=b-a. <O1OO2 is supplementary to <DPB because OO1 and OO2 perpendicular to AB and CD respective. That makes EO2OO1 a parallelogram.