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3 statements, one false, right triangle (2020 Novosibirsk Oral Geo Oly 8.3)

Source:

May 20, 2021
geometryright triangle

Problem Statement

Maria Ivanovna drew on the blackboard a right triangle ABCABC with a right angle BB. Three students looked at her and said: \bullet Yura said: "The hypotenuse of this triangle is 1010 cm." \bullet Roma said: "The altitude drawn from the vertex BB on the side ACAC is 66 cm." \bullet Seva said: "The area of the triangle ABCABC is 2525 cm2^2." Determine which of the students was mistaken if it is known that there is exactly one such person.