Saturday, February 23, 2019

Geometry Problem 1413: Right Triangle, Incircle, Excircle, Tangency Points, Isosceles Right Triangle

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

Details: Click on the figure below.

Geometry Problem 1413: Right Triangle, Incircle, Excircle, Tangency Points, Isosceles Right Triangle, Tutoring.

Posted by Antonio Gutierrez at 3:36 AM
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4 comments:

  1. c.t.e.oFebruary 23, 2019 at 5:36 AM

    ∆DJG ~ ∆JPT P, T tg points of E

    ReplyDelete
  2. Sumith PeirisFebruary 24, 2019 at 1:08 AM

    If the excircle touches AB at X and AC at Y, GDXY is an isosceles trapezoid with < YDG = 45 from my solution to Problem 1412

    So < DGX = < GXY = < GDY = 45

    Hence DJG is an isosceles right triangle

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
  3. Peter TranFebruary 24, 2019 at 10:00 AM

    https://photos.app.goo.gl/HgJdLL7rR8Aux4zz5

    connect AIE and IC
    we have ∠ (AIC)=135 => ∠ (EIC)=45 => ∠ (DGF)= 45
    CH= p-AC=BF ( p= half perimeter of trị ABC)
    DICH is a parallelogram => DH//IC and DH⊥FG
    So DGJ is isosceles right triangle

    ReplyDelete
  4. UnknownAugust 11, 2020 at 11:32 AM

    Pero se asume que YHJD son coloniales?

    ReplyDelete

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