Let A ABC be such that AB is not congruent to AC. Let D be the...

  

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Let A ABC be such that AB is not congruent to AC. Let D be the point of intersection of the bisector of LA and the perpendicular bisector of side BC. Let E, F, and G be the feet of the perpendiculars dropped from D to AB, AC, BC, respectively. Prove that: (a) D lies outside the triangle on the circle through ABC. (b) One of E, F lies inside the triangle and the other outside. (c) E, F, and G are collinear. C F G A D 0 E B Let A ABC be such that AB is not congruent to AC. Let D be the point of intersection of the bisector of LA and the perpendicular bisector of side BC. Let E, F, and G be the feet of the perpendiculars dropped from D to AB, AC, BC, respectively. Prove that: (a) D lies outside the triangle on the circle through ABC. (b) One of E, F lies inside the triangle and the other outside. (c) E, F, and G are collinear. C F G A D 0 E B