Question

Касательная к окружности параллельна хорде. Найдите радиус окружности, если известно, что длина хорды равна 6 см, а расстояние от точки касания до одного из концов хорды равно 5 см.

Answer 1

 Радиус перпендикулярный к хорде делить хорду пополам ,  то есть $3;3$ тогда часть диаметра окружность  будет равна $\sqrt{5^2-3^2}=4$ ,  положим что радиус равен $R$ , получим  по свойству хорд 
 $4(2R-4)=3^2\\ 8R-16=9\\ 8R=25\\ R=\frac{25}{8}$
 

Answer 2

Решение на двух фото, смотри в прикрепленных 

Answer 3

Problem Analysis

We are given that a tangent to a circle is parallel to a chord. The length of the chord is 6 cm, and the distance from the point of tangency to one of the chord's endpoints is 5 cm. We need to find the radius of the circle.

Solution

Let's denote the center of the circle as O, the point of tangency as A, and the endpoints of the chord as B and C. We are given that AB = 6 cm and OA = 5 cm.

To find the radius of the circle, we can use the property that the tangent to a circle is perpendicular to the radius at the point of tangency. Therefore, triangle OAB is a right triangle.

Using the Pythagorean theorem, we can find the length of OB, which is the radius of the circle.

Calculation

Let's calculate the length of OB using the Pythagorean theorem:

OB^2 = OA^2 - AB^2

OB^2 = 5^2 - 6^2

OB^2 = 25 - 36

OB^2 = -11

Since the square of a real number cannot be negative, we conclude that there is no real solution for the radius of the circle. It is not possible to have a circle with the given conditions.

Conclusion

Based on the given information, there is no real solution for the radius of the circle. It is not possible to have a circle with a tangent parallel to a chord with a length of 6 cm and a distance of 5 cm from the point of tangency to one of the chord's endpoints.