75. Extended Steinbart Theorem.

by Virgil Nicula, Aug 2, 2010, 11:42 PM

Quote:
Steinbart Theorem. Let $P$ be a point inside the incircle $w$ of $ABC$ . $w$ touches $\triangle ABC$ at $D\in BC$ , $E\in CA$ , $F\in AB$ . Let lines $DP$ , $EP$ , $FP$ meet $w$ again at $D_1$ , $E_1$ , $F_1$ . Show that $AD_1$ , $BE_1$ , $CF_1$ are concurrent.
Quote:
Extended Steinbart Theorem. Let $ABC$ be a triangle and $A'B'C'$ its tangential triangle. Let $A''$ , $B''$ , $C''$ be any points on the circumcircle of $\triangle ABC$ . Then $A'A''$ , $B'B''$ , $C'C''$ concur if and only if either $AA''$ , $BB''$ , $CC''$ concur or $AA''\cap BC$ , $BB''\cap CA$ , $CC''\cap AB$ are collinear.
This post has been edited 2 times. Last edited by Virgil Nicula, Nov 23, 2015, 3:31 PM

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