Составьте уравнение окружности с центром в точке к(-1; 3), проходящей через точку м(1; 5)

(x+1)^2 + (y - 3)^2 = 8

australia is the only country in the world that is also a continent. it is the sixth largest country and the smallest continent. it lies between the south pacific ocean and the indian ocean. the name of the country comes from latin word "australis" which means "southern". the country's official name is commonwealth of australia.

the commonwealth of australia is a federation of states. australia has six states — new south wales, queensland, south australia, tasmania, victoria and western australia. each state has its government.

about 23 million people live in australia nowadays. the natives of the country are called aborigines. now they occupy a very small part of the country’s population due to the former extrusion of the native people in the past.

the capital of australia is canberra. all the government buildings are situated there.

the capital is also the home of many cultural institutions, such as australian national university, national gallery, national museum, royal military college, australian institute of sport and many others.

the largest and the most visited city in australia is sydney. with the population of more than 4.6 million people. there is a great number of attractions in sydney. the most well–known ones are sydney opera house, sydney harbour bridge, st. mary's catholic cathedral and others.

the country has some unique species of animals, which can’t be found anywhere else. among them, koalas, kangaroos, wallabies, flightless emus, wombats and many others. so, the australian zoos can be another place of interest for tourists.

1.

Дано АС=АВ, ВД=СД

Доказать: ΔАВД= Δ АСД

Доказательство :Так как АС=АВ, ВД=СД и сторона АД- общая, то по 3-му признаку равенства треугольников( если три стороны одного треугольника соответственно равны трем сторонам другого, то такие треугольники равны) ΔАВД= Δ АСД

2)Пусть  основание треугольника -х, тогда (х+2)- боковая сторона.

По условию задачи составим уравнение:

х+(х+2)+(х+2)=40;

3х+4=40

3х=40-4

х=36:3

х=12 (см)- основание

х+2=12+2=14 (см) боковая сторона

ответ: 12 см, 14 см, 14 см.

4 задача:

так как∠BST=∠AST,  ∠STB=∠STA и ST- общая сторона, то ΔBST=ΔAST( по 2-му признаку : сторона и два прилежащих к ней угла равны).

Так как ΔBST=ΔAST, то BT=AT, КТ- общая сторона и  ∠STB=∠STA, то по 1-му признаку подобия : две стороні и угол между ними)  ΔКАТ=∠КВT, следовательно ВК=АК.