Simple concurrency

In $\Delta ABC$ , let $D$ be any point on $\overline{BC}$ .Let $\overline{DF} \ , \ \overline{DE}$ be bisectors of $\angle ADB \ , \ \angle ADC$ respectively with $E \in \overline{AC} \ , \ F \in \overline{AB}$ . Prove that $\overline{AD} \ , \ \overline{BE} \ , \ \overline{CF}$ are concurrent.

Posed this while playing with a theorem ;)

#Geometry

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Comments

Angle bisector theorem and cevas

Xuming Liang - 5 years, 9 months ago

Ah , I knew you would get it quickly. I used Ceva's instead of Menelaus. Nevermind Ceva's and Menelaus are brothers ;) :P