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triangle inequality with integer AC in ABC, ACD (2014 Kyiv City MO 7.4.1)

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August 5, 2020
triangle inequalitygeometrygeometric inequality

Problem Statement

The sides of triangles ABCABC and ACDACD satisfy the following conditions: AB=AD=3AB = AD = 3 cm, BC=7BC = 7 cm, DC=11DC = 11 cm. What values can the side length ACAC take if it is an integer number of centimeters, is the average in ΔACD\Delta ACD and the largest in ΔABC\Delta ABC?
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