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2006 China Second Round Olympiad Test 1 #1

Source:

September 28, 2014

Problem Statement

Let △ABC\triangle ABC be a given triangle. If ∣BA−tBC∣≥∣AC∣|BA-tBC| \ge |AC| for any t∈Rt \in \mathbb{R}, then △ABC\triangle ABC is <spanclass=′latex−bold′>(A)</span> an acute triangle<spanclass=′latex−bold′>(B)</span> an obtuse triangle<spanclass=′latex−bold′>(C)</span> a right triangle<spanclass=′latex−bold′>(D)</span> not known <span class='latex-bold'>(A)</span>\ \text{an acute triangle}\qquad<span class='latex-bold'>(B)</span>\ \text{an obtuse triangle}\qquad<span class='latex-bold'>(C)</span>\ \text{a right triangle}\qquad<span class='latex-bold'>(D)</span>\ \text{not known}\qquad
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