Friday, June 30, 2017

Geometry Problem 1336: Right Triangle, Cevian, Double Angle, Perpendicular, 90 Degrees

Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

This entry contributed by Sumith Peiris, Moratuwa, Sri Lanka.

Details: Click on the figure below..

Geometry Problem 1336: Right Triangle, Cevian, Double Angle, Perpendicular, 90 Degrees.

Posted by Antonio Gutierrez at 1:28 PM
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2 comments:

  1. UnknownJuly 1, 2017 at 3:39 AM

    triangulo BDE es isosceles (BD=DE), luego CDE es isosceles (CD=DE).
    por tanto, BE es perpendicular a AC.

    ReplyDelete
  2. AnonymousJuly 2, 2017 at 9:49 AM

    <EBC=90°-a
    By angle sum of triangle EBD,
    <DEB=90°-a
    Hence DE=DB
    Because DB=DC
    So DE=DC
    Hence <DEC={180°-(180°-2a)}/2
    <DEC=a
    Hence <BEC=(90°-a)+a=90°

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