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MB = MC wanted, angle bisector, perpendiculars (2015 Kyiv City MO 11.4.1)

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September 3, 2020
geometryangle bisectorequal segmentsperpendicular

Problem Statement

On the bisector of the angle BAC BAC of the triangle ABC ABC we choose the points B1,  C1 {{B} _ {1}}, \, \, {{C} _ {1}} for which BB1⊥AB B {{B} _ {1 }}\perp AB , CC1⊥AC C {{C} _ {1}} \perp AC . The point M M is the midpoint of the segment B1C1 {{B} _ {1}} {{C} _ {1}} . Prove that MB=MC MB = MC .
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