1. In triangle ABC with pedal triangle DEF (such that D, E, F are the feet of the altitudes from A, B, C to the opposite sides respectively), let P be the intersection of AD and EF. Prove that P is the orthocenter of triangle AQR, and that A, Q, D, R are concylic.
2. For a triangle ABC, let D, E, F be on BC, CA, AB respectively.
BD/DC=CE/EA=AF/FB, angle BAC= angle EDF.
Show that triangle ABC is similar to triangle DEF.
2. For a triangle ABC, let D, E, F be on BC, CA, AB respectively.
BD/DC=CE/EA=AF/FB, angle BAC= angle EDF.
Show that triangle ABC is similar to triangle DEF.