Wednesday, November 25, 2020

Geometry Problem 1485: Triangle, Orthocenter, Altitude, Circle, Diameter, Tangent, Measurement

Geometry Problem 1485. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

Geometry Problem 1485: Triangle, Orthocenter, Altitude, Circle, Diameter, Tangent, Measurement.

Posted by Antonio Gutierrez at 4:48 AM
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4 comments:

  1. Peter TranNovember 25, 2020 at 4:18 PM

    https://photos.app.goo.gl/v7KgdZECAesRBJjr9
    Draw altitude BD of triangle ABC ( see sketch)
    We have B, H, D are collinear ( H is the orthocenter)
    Quadrilateral ADEB is cyclic so HE.HA=HB.HD= 140
    In cycle BTDC we have HT.HF=HB.HD=140
    So HF= 140/HT=8.5

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    Replies
    1. Peter TranNovember 27, 2020 at 8:09 AM

      minor correction of the last line:

      So HF= 140/HT=8.75

      Delete
  2. c.t.e.o.November 26, 2020 at 12:40 AM

    Draw altitude BP
    We have BH . HP = 140
    => TH . HF = 140 => HF = 8.75

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