Geometry Problem. Post your solution in the comment box below.

Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

## Saturday, February 23, 2019

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

Labels:
excircle,
geometry problem,
incircle,
isosceles,
right triangle,
tangency point

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∆DJG ~ ∆JPT P, T tg points of E

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

ReplyDeleteSo < DGX = < GXY = < GDY = 45

Hence DJG is an isosceles right triangle

Sumith Peiris

Moratuwa

Sri Lanka

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

ReplyDeleteconnect AIE and IC

we have ∠ (AIC)=135 => ∠ (EIC)=45 => ∠ (DGF)= 45

CH= p-AC=BF ( p= half perimeter of trá»‹ ABC)

DICH is a parallelogram => DH//IC and DH⊥FG

So DGJ is isosceles right triangle

Pero se asume que YHJD son coloniales?

ReplyDelete