Question

Плоскость проходит через точку A и касается сферам центром Oи радиусом 3 см.Определите расстояние от этой точки до точки касания, если OA=5 см. Помогите пожалуйста)))

Answer 1

Пусть точка касания - это точка К,
Тогда по теореме Пифагора: АК = корень с (25 - 9) = 40/0точка касания (К) , ОК=3 см, ОА=5 см. Далее по теореме Пифагора.
а2 + в2= с2, АК= 25-9 (извлечь корень) . У тебя ведь не сказано под каким углом касательная идет к радиусу. Может она перпендикулярна.

Answer 2

Problem Analysis

We are given that a plane passes through point A and is tangent to spheres with center O and radius 3 cm. We need to determine the distance from point A to the point of tangency, given that OA = 5 cm.

Solution

To solve this problem, we can use the concept of similar triangles. Let's consider the right triangle formed by the line segment OA, the distance from point A to the point of tangency, and the radius of the sphere.

Let the distance from point A to the point of tangency be x cm. We can set up the following proportion:

OA / x = radius of the sphere / radius of the sphere + x

Substituting the given values, we have:

5 / x = 3 / (3 + x)

To solve for x, we can cross-multiply and solve the resulting equation:

5(3 + x) = 3x

15 + 5x = 3x

15 = 3x - 5x

15 = -2x

x = -15 / 2

Since distance cannot be negative, we discard the negative solution. Therefore, the distance from point A to the point of tangency is 15/2 cm.

Answer

The distance from point A to the point of tangency is 15/2 cm.