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.Problem submitted by Maurice HoClick the diagram below to enlarge it.
Let AB=a, BC=b, CDgc, DA=d. Thena²+b² = c²+d²a+c = b+da-b = d-csquare then gives ab=cdThus a+b=d+cHence, a=d and b=c. Area = 1/2 r(a+b+c+d) = r(a+b)
Area ABCD=2 Area ABC(deoarece A,OsiC sunt coliniare)=2(AreaAOB+AreaBOC)=2(AB.r/2+BC.r/2)=r(AB+BC)
We can see there are two squares OT_1BT_2 and OT_3DT_4. That means AB=AD and BC=BD.(ABCD)=(ABO)+(BOC)+(COD)+(DOA)=1/2 r( AB+BC+CD+DA)=R(AB+BC)
It also follows that r^2,= AT1. CT2