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Additional problem 1 Let AABC be a triangle, let be the bisector of the angle ZCAB Let P be the intersection of and BC. Let R be the point on the line AB such that AR-AC, and let X-APnRC. Let Q denot...

Additional problem 1 Let AABC be a triangle, let be the bisector of the angle ZCAB Let P be the intersection of and BC. Let R

Additional problem 1 Let AABC be a triangle, let be the bisector of the angle ZCAB Let P be the intersection of and BC. Let R be the point on the line AB such that AR-AC, and let X-APnRC. Let Q denote the intersection point between the line through B and X and AC. (a) Show that the triangle AARC is isosceles, and deduce that RX-XC. (b) Apply Menelaus's theorem to the triangle AARC with the line through B, X, and Q, and deduce a relation between AB, CQ, RB, and QA c) Write the result of applying Ceva's theorem on AABC with the point X (d) Prove that AB PC- AC BP NOTE: for this exercises it is more convenient to work with positive ratios rather than signed ratios (so the -1 in Menelaus's theorem would become a +1).
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AMognence R8 OAConseer, △ABC (c) Ceva theerem by Ceva R PC OA c) from )AB.PC AR BP

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Additional problem 1 Let AABC be a triangle, let be the bisector of the angle ZCAB Let P be the intersection of and BC. Let R be the point on the line AB such that AR-AC, and let X-APnRC. Let Q denot...
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