Problem :

Let $∆ABC$ triangle and $C(D,ED)$ excircle of triangle $ABC$ , $r_{1}=ED$ also $C(G,GF)$ incircle of a triangle $ABC$, $GF=r_2.$

$d=$ distance between centers of the two circles $d=d(D,G)$

Then prove that : $$r_{1}^{2}=d^{2}+2r_{1}r_{2}$$

I know the center of the incircle can be found as the intersection of the three internal angle bisectors and The center of an excircle is the intersection of the internal bisector of one angle

But I don't know which relations I must use to prove the above relationsenter image description here


See Euler's theorem for the triangle.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.