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В окружность вписан выпуклый четырёхугольник, последовательные стороны которого равны а, b, с и d. Доказать, что площадь его равна корень(р-а)(р-в)(р-с)(р-d) где р=1/2(a+b+c+d) Доказать, что если в этот четырёхугольник можно вписать окружность, то его площадь равна корень(abcd) .
В окружность вписан выпуклый четырёхугольник, последовательные стороны которого равны а, b, с и d. Доказать, что площадь его равна корень(р-а)(р-в)(р-с)(р-d) где р=1/2(a+b+c+d)
На самом деле выражение для площади четырёхугольника, вписанного в окружность, имеет вид
и называется формулой Брахмагупты. Её доказательство есть здесь.
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semalina 
