Geometry · Angle bisector · Congruent triangles · Perpendicular bisector · Trapezoid midline
On the bisector of the angle \(\angle BAC\) of a triangle \(ABC\), points \(B_1\) and \(C_1\) are chosen so that \(BB_1 \perp AB\) and \(CC_1 \perp AC\). Let \(M\) be the midpoint of the segment \(B_1C_1\). Prove that \(MB = MC\).
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Serbian Municipal Competition 2007, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source