Question

ОЧЕНЬ СРОЧНО НУЖНА ПОМОЩЬ! С2 Отрезок KM – диаметр основания конуса, отрезок AK – образующая этого конуса, которая в 3 раза больше радиуса его основания. Хорда основания ML составляет с прямой KM угол 45*. Через AK проведено сечение конуса плоскостью, параллельной прямой ML. Найдите расстояние от центра основания конуса O до плоскости сечения, если радиус основания конуса равен 1.

Answer 1

Пусть отрезок KN ― хорда основания, параллельная ML. Тогдатреугольник AKN ― искомое сечение, так как плоскость AKNсодержит прямую AK и прямую KN, параллельную ML. Опустимперпендикуляр AB на прямую KN. Согласно теореме о трехперпендикулярах OB также является перпендикуляром к KN,значит, KN ⊥ (ABO) . Высота OC треугольника ABO лежит вплоскости ABO, следовательно, OC ⊥ AB и OC ⊥ KN , а, значит, OC ⊥ (AKN).
Далее находим:
1) из условия KN \\ML : ∠NKM = ∠KML = 45°
2) из прямоугольного треугольника KON: OB = (KO*КОРЕНЬ ИЗ 2)\2=(КОРЕНЬ ИЗ 2)\2
3) из прямоугольного треугольника AKO:  AO^2 = AK^2 − KO^2 = 9R^2 − R^2 = 8
4) из прямоугольного треугольника ABO:  а) AB =  КОРЕНЬ ИЗ (OB^2 + AO^2  ) = (КОРЕНЬ ИЗ 34)\2
б)OC= (OB *OA)\AB=(√2*2√2*2)\2*√34=4\√34
ОТВЕТ:4\√34
 

Answer 2

Problem Analysis

We are given a cone with base diameter KM and slant height AK, which is three times the radius of the base. The chord of the base ML forms a 45-degree angle with the line KM. A section of the cone is made by a plane parallel to the line ML. We need to find the distance from the center of the base of the cone (point O) to the plane of the section.

Solution

To solve this problem, we can break it down into smaller steps:

1. Find the radius of the base of the cone. 2. Find the length of the chord ML. 3. Find the distance from the center of the base of the cone to the plane of the section.

Let's solve each step one by one.

Step 1: Find the radius of the base of the cone

We are given that the slant height AK is three times the radius of the base. Let's assume the radius of the base is r. Therefore, the slant height AK is 3r.

Step 2: Find the length of the chord ML

We are given that the angle between the chord ML and the line KM is 45 degrees. Since the chord ML is perpendicular to the diameter KM, it divides the diameter into two equal parts. Therefore, the length of the chord ML is equal to the radius of the base of the cone, which we assumed to be r.

Step 3: Find the distance from the center of the base of the cone to the plane of the section

To find the distance from the center of the base of the cone to the plane of the section, we need to find the perpendicular distance from the center of the base to the plane of the section. This distance is equal to the radius of the base of the cone, which we assumed to be r.

Therefore, the distance from the center of the base of the cone to the plane of the section is r.

Answer

The distance from the center of the base of the cone (point O) to the plane of the section is equal to the radius of the base of the cone, which is r.

Please note that the specific numerical value of r is not provided in the question, so we cannot calculate the exact distance. However, we can conclude that the distance is equal to the radius of the base of the cone.

I hope this helps! Let me know if you have any further questions.