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.

4 comments:

  1. ∆DJG ~ ∆JPT P, T tg points of E

    ReplyDelete
  2. 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. 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. Pero se asume que YHJD son coloniales?

    ReplyDelete