Wednesday, July 15, 2015

Geometry Problem 1137: Triangle, Circumcircle, Orthocenter, Midpoint, Arc, Collinear Points, Tangent Circles

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.

Online Math: Geometry Problem 1137: Triangle, Circumcircle, Orthocenter, Midpoint, Arc, Collinear Points, Tangent Circles.

1 comment:

  1. http://s14.postimg.org/j7s4od1u9/pro_1137.png

    Draw points P, Q, S per attached sketch
    Observe 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 QHF
    S is the circumcenter of triangle QHF
    In right triangle MHS with altitude HD we have SH^2=SF^2=SD.SM
    So SF tangent to circuncircle of MDF
    SH ⊥ HE and SH=SF => SF tangent to circumcircle of HFE
    So SF is tangent to both circles O1 and O2

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