Unformatted text preview: a + b + c ) . 5. (IMO 1964) Suppose that a , b , and c are the lengths of the sides of a triangle. Prove that a 2 ( b + ca ) + b 2 ( a + cb ) + c 2 ( a + bc ) ≤ 3 abc. 6. Let D be the foot of the bisector of ∠ A of 4 ABC . Prove that BD : DC = BA : AC . 7. Given the value of a and the measures of the angles B and C of 4 ABC , express ( ABC ) in terms of the given quantities. 8. Let ABC be a triangle. Prove that sin A 2 ≤ a b + c 9. (IMO 1996) Let P be a point inside 4 ABC such that ∠ APB∠ C = ∠ APC∠ B . Let D and E be the incenters of 4 APB and 4 APC , respectively. Show that the lines AP , BD , and CE are concurrent....
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 Spring '09
 B
 Equations, Pythagorean Theorem, Law Of Cosines, triangle

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