Question

До кола із центром О провели дотичну АВ ( А-точка дотику). Знайдіть радіус кола, якщо ВО=11 см і кут ВОА=60 градусів​

Answer 1

Problem Analysis

We are given a circle with center O and a tangent line AB. We need to find the radius of the circle if VO = 11 cm and angle VOA = 60 degrees.

Solution

To find the radius of the circle, we can use the properties of tangents and angles in a circle.

First, let's draw a diagram to visualize the problem:

         A
        /
       /
      O
     /
    /
   B

From the given information, we know that VO = 11 cm and angle VOA = 60 degrees.

Since AB is a tangent to the circle, the radius of the circle is perpendicular to AB at the point of tangency, which is point A in this case.

Let's denote the radius of the circle as r.

Using trigonometry, we can find the length of AB in terms of r and the given angle VOA.

In a right triangle OVA, we have:

sin(VOA) = AB / VO
sin(60) = AB / 11

Simplifying the equation:

AB = 11 * sin(60)

Now, we can use the fact that#### Problem Analysis We are given a circle with center O and a tangent line AB. We need to find the radius of the circle if VO = 11 cm and angle VOA = 60 degrees.

Solution

To find the radius of the circle, we can use the properties of tangents and the relationship between the radius and the tangent line.

Let's consider the triangle VOA. We know that VO = 11 cm and angle VOA = 60 degrees. We need to find the radius of the circle, which is the line segment OA.

Using trigonometry, we can find the length of OA. In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the hypotenuse. In this case, the hypotenuse is VO and the side opposite the angle is OA.

Using the sine function, we have:

sin(60 degrees) = OA / VO

Simplifying the equation, we have:

OA = VO * sin(60 degrees)

Substituting the given values, we have:

OA = 11 cm * sin(60 degrees)

Using a calculator, we can find the value of sin(60 degrees) to be approximately 0.866.

OA = 11 cm * 0.866

OA ≈ 9.526 cm

Therefore, the radius of the circle is approximately 9.526 cm.

Answer

The radius of the circle is approximately 9.526 cm.