Saturday, February 23, 2019

Geometry Problem 1415: Right Triangle, Altitude, Incircle, Excircle, Tangency Points, Isosceles 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 1415: Right Triangle, Altitude, Incircle, Excircle, Tangency Points, Isosceles Triangle, Tutoring.
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3 comments:

  1. c.t.e.oFebruary 23, 2019 at 6:02 AM

    ∆JBF isosceles => ∆JGB isosceles

    ReplyDelete
  2. Sumith PeirisFebruary 24, 2019 at 7:47 AM

    < BFJ = C/2 from Problem 1410 and < ABJ = C so < BJF = C/2 and hence BJ = BF = BG

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
  3. Peter TranFebruary 24, 2019 at 9:42 AM

    https://photos.app.goo.gl/yqpR9Fb7fB8CnjAw6
    Define points L ,K and angle u per sketch
    Per the results of previous problems we have ICE is a isosceles right triangle and DJ ⊥IC
    We have GC= p-AC= BD ( p= half perimeter of trị ABC)
    Triangle EGC congruent to FBD( case SAS)
    So ∠ (BFD)= ∠ (GEC)=u
    We also have ∠ (HCI)=u=∠ (BJD)=∠ (BFJ)=> JBF is isosceles
    But BG=BF= BJ => JBG is isosceles

    ReplyDelete

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