Geometry · Triangle · Altitude · Thales circle · Angle comparison
Problem 1, 2013
In a triangle \(ABC\), the altitude from \(A\) meets the line \(BC\) at \(D\), and its length satisfies
\[ AD = \tfrac{1}{2}\,BC. \]
Prove that the angle of the triangle at the vertex \(A\) cannot be obtuse.
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Serbian Municipal Competition 2013, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source