Online Geometry theorems, problems, solutions, and related topics.
Geometry Problem. Post your solution in the comment box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the figure below to view more details of problem 1245.
https://goo.gl/photos/Raksk92QKNNeK9wC6Observe that OE, OF , OG and OH perpendicular to AB, BC, CD and AD.Draw diameter FF’We have ∠ (EOF’)= ∠ (B) … ( both angles supplement to ∠ (EOF) )∠ (HOG)= ∠ (B)…. ( both angles supplement to∠ (D)) Triangles EOF’ congruent to HOG ( case SAS) => EF’= HGIn right triangle FEF’ we have EF^2+EF’^2= EF^2+HG^2= 36+16= 52= 4. Radius^2Similarly FG^2+EH^2= 4. Radius^2= 25+x^2So x^2= 52-25=27 and x=3.sqrt(3)
Notice that GE_|_FH, thus EF^2+GH^2=FG^2+EH^2, wherefrom x^2=27.Best regards