Question

До кола з центром O проведено дотичну CD (D-точка дотику). Знайдіть радіус кола , якщо Cd = 16 см и кут COD = 60° Срочно пж!! Даю 40б

Answer 1

ОД-перпендикуляр в точку дотику=радіус кола, кут СОД=60, трикутник СОД прямокутний, кут С=90-60=30, СО-гіпотенуза=16, тоді ОД=1/2СО=16/2=8, як катет який лежит проти кута 30.
не знаю вроде так сори если не правильно (

Answer 2

Problem Analysis

We are given that a circle with center O is tangent to a line CD at point D. We need to find the radius of the circle given that CD = 16 cm and angle COD = 60°.

Solution

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

1. Draw a diagram: - Draw a circle with center O. - Draw a line CD tangent to the circle at point D. - Mark the point of tangency as T.

2. Identify the given information: - CD = 16 cm - COD = 60°

3. Use the properties of tangents: - The line segment from the center of a circle to the point of tangency is perpendicular to the tangent line. - Therefore, angle COD is a right angle.

4. Use trigonometry to find the radius: - 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 triangle COD, the side opposite angle COD is CD and the hypotenuse is the radius of the circle. - We can use the sine function to find the radius: ``` sin(COD) = CD / radius ``` - Substituting the given values: ``` sin(60°) = 16 cm / radius ```

5. Solve for the radius: - We can rearrange the equation to solve for the radius: ``` radius = 16 cm / sin(60°) ```

6. Calculate the radius: - Using a calculator, we can evaluate the expression: ``` radius ≈ 18.37 cm ```

Answer

The radius of the circle is approximately 18.37 cm.

Please note that the source provided does not contain relevant information for this specific problem.