Question

Радиус окружности с центром в точке О равен 10 см, длина хорды АВ равна 16 см. Найдите расстояние от хорды АВ до параллельной ей касательной Л

Answer 1

РЕШЕНИЕ ПРИВЕДЕНО ВО ВЛОЖЕНИИ

Answer 2

Problem Analysis

We are given the following information: - The radius of a circle with center O is 10 cm. - The length of chord AB is 16 cm.

We need to find the distance from chord AB to a parallel tangent line L.

Solution

To find the distance from chord AB to the parallel tangent line L, we can use the following steps:

1. Draw a diagram of the given information. Let O be the center of the circle, AB be the chord, and L be the parallel tangent line.

2. Draw a line segment from the center O to the midpoint M of chord AB. This line segment will be perpendicular to chord AB.

3. Since OM is perpendicular to AB, it bisects AB. Therefore, the length of OM is half the length of AB, which is 8 cm.

4. Draw a line segment from the center O to a point P on the parallel tangent line L. This line segment will be perpendicular to L.

5. Since OP is perpendicular to L, it is also the shortest distance from chord AB to line L.

6. To find the length of OP, we can use the Pythagorean theorem. In triangle OMP, OM is the perpendicular side, MP is the base, and OP is the hypotenuse.

Using the Pythagorean theorem, we have: OP^2 = OM^2 + MP^2

Substituting the known values, we have: OP^2 = 8^2 + MP^2

Simplifying, we have: OP^2 = 64 + MP^2

7. To find MP, we can use the fact that MP is half the length of AB. Therefore, MP = AB/2 = 16/2 = 8 cm.

8. Substituting the value of MP into the equation from step 6, we have: OP^2 = 64 + 8^2 OP^2 = 64 + 64 OP^2 = 128

9. Taking the square root of both sides, we have: OP = √128

10. Simplifying, we have: OP ≈ 11.31 cm

Therefore, the distance from chord AB to the parallel tangent line L is approximately 11.31 cm.

Conclusion

The distance from chord AB to the parallel tangent line L is approximately 11.31 cm.