Question

К окружности радиуса 10 см проведена касательная, на которой взята точка М на расстояние 24 см от точки касания. Найдите расстояние от точки М до центра окружности.

Answer 1

1) Для начала вам следует сделать чертёж. Затем вспомнить, что касательная в точке касания образует прямой угол с радиусом, то есть у вас получается прямоугольный треугольник с катетами 24 см и 10 см.

 

2) Найдём расстояние от точки до центра окружности по теореме Пифагора:

корень из (100 + 576) = 26 (см)

 

Ответ: расстояние 26 см. 

Answer 2

Problem Analysis

We are given a circle with a radius of 10 cm. A tangent is drawn to the circle, and point M is taken on the tangent, 24 cm away from the point of contact. We need to find the distance from point M to the center of the circle.

Solution

To solve this problem, we can use the properties of tangents and radii in a circle.

Let O be the center of the circle, and let T be the point of contact between the tangent and the circle. We are given that the radius of the circle is 10 cm, so OT = 10 cm.

We are also given that point M is 24 cm away from point T. Let's call the distance from point M to the center of the circle OM.

According to the properties of tangents, the tangent line is perpendicular to the radius at the point of contact. Therefore, triangle OTM is a right triangle.

Using the Pythagorean theorem, we can find the length of OM:

OM^2 = OT^2 - TM^2

Substituting the given values:

OM^2 = 10^2 - 24^2

Simplifying:

OM^2 = 100 - 576

OM^2 = -476

Since the result is negative, it means that the distance OM is an imaginary number. This implies that the point M is outside the circle, beyond the reach of the radius.

Therefore, there is no valid solution for the given problem.

Conclusion

The distance from point M to the center of the circle cannot be determined because point M is located outside the circle.