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Leo tolstoy was born on 9 sentyabrya year. "young loew has been in musclemania four years. in july 1837 suddenly his father died. (mother tolstoy died when he was two years old.) orphaned children moved to kazan, where she was their guardian, aunt p. i. yushkova. tolstoy lived in kazan six years. that was the time of his adolescence and youth. two and a half years he was preparing to enter the university. deciding to become a diplomat, tolstoy sat exams on the east branch. he successfully passed the exams on the history, geography, mathematics, statistics, russian literature, logic, english, french, german, latin, arabic, turkish and tatar languages. already in the time of leo tolstoy showed exceptional ability to learn foreign languages. later, the sister of the writer was talking about. professor hired as a senior teacher with whom tolstoy studied turkish and tatar languages, found his ability to master languages extraordinary."

а) Если известно, что АС=12, то МВ = АС/3 = 12/3 = 4.
Медиана ВВ1 равна (3/2) длины отрезка ВМ.
ВВ1 = (3/2)*4 = 6.
Как видим, медиана равна половине стороны АС. Поэтому треугольник АВС - прямоугольный, а АС - гипотенуза.

б) Сумма квадратов катетов АВ и ВС равна квадрату АС, то есть 12² = 144.

Если нужна сумма квадратов медиан, проведенных к катетам, то решение такое:
Пусть АВС - исходный треугольник, С - вершина прямого угла, а АЕ и ВD - медианы.
Пусть  ВС = а, АС = b.  Тогда по теореме Пифагора
ВD² = BC² + CD² = a² + (b/2)² = a² + b²/4
AE² = AC² + CE² = b² + (a/2)² = b² + a²/4
Следовательно 
BD² + CE² = a² + b²/4 + b² + a²/4 = 5/4 * (a² + b²) = 5/4 * AB².

Это копия с задания 359967.