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

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

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## Thursday, August 9, 2018

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

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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

ReplyDeleteSumith Peiris

Moratuwa

Sri Lanka

https://photos.app.goo.gl/U9fbGryQ5jtheoD6A

ReplyDeleteSee 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