tag:blogger.com,1999:blog-6933544261975483399.post5859259553263141373..comments2024-03-19T00:02:30.728-07:00Comments on Go Geometry (Problem Solutions): Geometry Problem 991: Triangle, Incircle, Tangent Points, Isosceles, Midpoint, Collinearity, Congruence, CircleAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-6933544261975483399.post-3553906533957274212014-03-11T11:13:41.997-07:002014-03-11T11:13:41.997-07:00Let altitude BK of triangle ABC cut EF at N and AC...Let altitude BK of triangle ABC cut EF at N and AC at K<br />let incircle I tangent to AC at L<br />Let p and p’ are haft perimeter of triangles BDC and ABC <br />Using properties of incircles I , I1 and isosceles triangle ABD we have LE= p’-p => LE=AK=KD<br />We also have ∠(DEF)=1/2∠(FDA)= ∠(IAL) and AL=KE<br />Triangles ALI congruent to EKN => KLIN is a rectangle <br />Since DE=KL=NI => DEIN is a parallelogram and diagonals will bisect each other.<br />Peter Tranhttps://www.blogger.com/profile/02320555389429344028noreply@blogger.com