Thursday, August 9, 2018

Geometry Problem 1377: Isosceles Triangle, Interior Cevian, Equal Sum of Exradii, Excircles

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 1377: Isosceles Triangle, Interior Cevian, Equal Sum of Exradii, Excircle.

Posted by Antonio Gutierrez at 8:43 PM
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2 comments:

  1. Sumith PeirisAugust 10, 2018 at 1:45 AM

    This result is easily inferred from the result of Problem 1375 ( Antonio I await your publishing of my proof of this) according to which the difference of the radii of 2 opposite excircles is equal to h, the height of the altitude from B of isosceles Tr. ABC

    Sumith Peiris
    Moratuwa
    Sri Lanka

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  2. Peter TranAugust 11, 2018 at 3:57 PM

    https://photos.app.goo.gl/U9fbGryQ5jtheoD6A
    See sketch for positions of points H, P, Q
    Per the result of problem 1375 we have O3Q= r3 and O1P=r4
    So r3-r2= h= r1-r4 and r1+r2=r3+r4

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