Thursday, August 18, 2016

Geometry Problem 1248: Triangle, Circumcircle, Circle, Diameter, Orthocenter, Altitude, Parallel Lines

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 1248.

Geometry Problem 1248: Triangle, Circumcircle, Circle, Diameter, Orthocenter, Altitude, Parallel Lines
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2 comments:

  1. Peter TranAugust 19, 2016 at 9:04 AM

    Connect KC,
    Quadrilateral AEDC is cyclic => ∠ (BED)= ∠ (ACB) .. ( both angles supplement to ∠ (AED))
    we have ∠ (BAC)= ∠ (BKC) => ∠ (ABF)= ∠ (KBC)
    so triangle BEG similar to BCM and triangles BEH similar to BCK …( case AA)
    and we have BG/BM=BE/BC=BH/BK
    so BG/BH=BM/BK
    and GM//HK

    ReplyDelete
  2. Peter TranDecember 9, 2022 at 4:49 PM

    add sketch of problem 1248

    https://photos.app.goo.gl/2rCpcFijxxBSHph78

    ReplyDelete

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