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equal segments from projections, altitudes related (2014 Kyiv City MO 10.4)

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August 6, 2020
geometryequal segmentsaltitudes

Problem Statement

The altitueds AA1A {{A} _ {1}} , BB1B {{B} _ {1}} and CC1C {C} _ 1 are drawn in the acute triangle ABCABC. . The perpendicular AKAK is drawn from the vertex AA on the line A1B1{{A} _ {1}} {{B} _ {1}}, and the perpendicular BLBL is drawn from the vertex BB on the line C1B1{{C} _ {1}} {{B} _ {1}}. Prove that A1K=B1L{{A} _ {1}} K = {{B} _ {1}} L.
(Maria Rozhkova)
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