Question

Дана прямая l и окружность с центром в точке О и точка А на окружности, прямая l не имеет общих точек с окружностью. Построить окружность, которая касается прямой l и касается окружности в точке А.

Answer 1

Какой радиус окружности?

Answer 2

Problem Description

Given a line l and a circle with center at point O and point A on the circle, where the line l does not intersect the circle, the task is to construct a circle that is tangent to the line l and tangent to the circle at point A.

Solution

To construct a circle that is tangent to the line l and tangent to the circle at point A, we can use the following steps:

1. Draw a line perpendicular to l passing through point A. Let's call this line m. 2. The circle we want to construct will have its center on line m and will pass through point A. 3. The distance from the center of the new circle to line l will be equal to the radius of the given circle.

Mathematical Explanation

The circle we want to construct will be tangent to the line l and tangent to the given circle at point A. This means that the distance from the center of the new circle to line l will be equal to the radius of the given circle. Additionally, the center of the new circle will lie on the line perpendicular to l passing through point A.

By following these steps, we can construct the required circle that is tangent to the line l and tangent to the given circle at point A.

I hope this helps! If you have further questions or need additional assistance, feel free to ask.