Assignment 2

# Assignment 2 - MATH 348 Assignment 2(nal version Leonid...

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MATH 348: Assignment 2 (final version) Leonid Chindelevitch July 15, 2008 1. Let the triangle ABC have circumradius R . Prove that its area is given by S = abc 4 R . Comment: This is an ordinary proof, so you may use the fact sheet. 2. Prove that the following statements are equivalent for the triangle ABC : 1) γ = π 2 (= 90 ); 2) C is the orthocenter of Δ ABC ; 3) the midpoint C of c is the circumcenter of Δ ABC . Comment: Try to solve this one Euclid style; note that to prove the equivalence of any three statements, it is enough to prove 1 = 2 = 3 = 1. However, this is not necessarily the most convenient way. 3. Prove that a parallelogram is a rhombus if and only if its diagonals are perpendicular. Comment: For questions 3 and 4, don’t forget to prove both directions!
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