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 diagram below to enlarge it.
http://s14.postimg.org/j7s4od1u9/pro_1137.pngDraw points P, Q, S per attached sketchObserve that H, M, P are collinear and AC is the perpendicular bisector of HQ. ( see other problem)With manipulation of angles we will get ∠ (EHF)= ∠ (BPF)= ∠ (HQS)= ∠ (QHS)= ∠ (SMH) …( see sketch)We will get the following results:HF//AC and MH tangent to circumcircle of triangle QHFS is the circumcenter of triangle QHFIn right triangle MHS with altitude HD we have SH^2=SF^2=SD.SMSo SF tangent to circuncircle of MDFSH ⊥ HE and SH=SF => SF tangent to circumcircle of HFESo SF is tangent to both circles O1 and O2