8. P△AMN = 48, AB, AC - ?

Треугольник AMN описан около окружности. Пусть AM = x, тогда AK = AM = x, MB = BK = y, CN = NC = z. P△AMN = AM + MN + AN = 48. AB = AM + MB = x + y. AC = AN + NC = x + z. MN = MK + KN = y + z. Тогда P△AMN = x + (y + z) + x = 2x + y + z = 48. P△ABC = AB + BC + AC = (x + y) + (y + z) + (x + z) = 2(x + y + z). 2x + 2y + 2z = 2(x + y + z) = 2 * 48 = 96. AB + AC = (AM + MB) + (AN + NC) = x + y + x + z = 2x + y + z = 48. AB + AC = 48. AB = AC. Пусть AB = AC = a. Тогда a + a = 48. 2a = 48. a = 24. AB = 24, AC = 24. Ответ: AB = 24, AC = 24