The kangaroo is a wild animal which has large, powerful hind legs, a long muscular tail and a small head. There are known over 60 different species of kangaroos and close relatives. Some of them can be two meters tall with weight up to 90 kg. The others are much smaller in size. Kangaroos are unusual and wonderful animals. Kangaroos hop like rabbits to move around quickly. They can jump as far as about three times their own height. They walk on four legs when there is no need to move fast. Kangaroos are called marsupials because they carry their babies in a special bag on their paunches. Kangaroos are herbivore animals, they eat mainly grass and shrubs. They are common in Australia. The kangaroo is one of the most well-known native Australian animals. Although it can also be found in New Guinea kangaroo is the iconic animal of Australia. It is even pictured on the coat of arms for Australia.
(ВС1/С1А)*(АР/РА1)*(А1С/СВ) = 1. Подставим известные соотношения: ВС1/С1А = 1/1 (СС1 - медиана), СА1/ВС=1/3 (СА1/А1В=1/2 - дано ). Тогда (1/1)*(АР/РА1)*(3/1) =1 => АР/РА1 = 3/1.
ответ: медиана СС1 делит отрезок АА1 в отношении АР:РА1 = 3:1.
Без применения формулы Менелая.
Проведем С1К параллельно ВС. С1К - средняя линия треугольника АВА1, так как точка С1 делит сторону АВ пополам, а отрезок КС1 параллелен стороне ВС по построению. Треугольники АС1К и АВА1 подобны с коэффициентом k=1/2. АК=КА1. Треугольники РС1К и РСА1 подобны с коэффициентом k=1/1 (то есть равны, так как СК=(1/2)*ВА1). КР=РА1.Тогда АР = 3*РА1. То есть отношение АР/РА1 = 3:1.
The kangaroo is a wild animal which has large, powerful hind legs, a long muscular tail and a small head. There are known over 60 different species of kangaroos and close relatives. Some of them can be two meters tall with weight up to 90 kg. The others are much smaller in size. Kangaroos are unusual and wonderful animals. Kangaroos hop like rabbits to move around quickly. They can jump as far as about three times their own height. They walk on four legs when there is no need to move fast. Kangaroos are called marsupials because they carry their babies in a special bag on their paunches. Kangaroos are herbivore animals, they eat mainly grass and shrubs. They are common in Australia. The kangaroo is one of the most well-known native Australian animals. Although it can also be found in New Guinea kangaroo is the iconic animal of Australia. It is even pictured on the coat of arms for Australia.
В треугольнике АВ1А1 по теореме Менелая:
(ВС1/С1А)*(АР/РА1)*(А1С/СВ) = 1. Подставим известные соотношения: ВС1/С1А = 1/1 (СС1 - медиана), СА1/ВС=1/3 (СА1/А1В=1/2 - дано ). Тогда (1/1)*(АР/РА1)*(3/1) =1 => АР/РА1 = 3/1.
ответ: медиана СС1 делит отрезок АА1 в отношении АР:РА1 = 3:1.
Без применения формулы Менелая.
Проведем С1К параллельно ВС. С1К - средняя линия треугольника АВА1, так как точка С1 делит сторону АВ пополам, а отрезок КС1 параллелен стороне ВС по построению. Треугольники АС1К и АВА1 подобны с коэффициентом k=1/2. АК=КА1. Треугольники РС1К и РСА1 подобны с коэффициентом k=1/1 (то есть равны, так как СК=(1/2)*ВА1). КР=РА1.Тогда АР = 3*РА1. То есть отношение АР/РА1 = 3:1.