Question

Прямая ВР касается окружности с центром О радиуса 6 в точке В. Найдите длину отрезка ВР если угол ВОР = 60

Answer 1

По свойству касательной ОВ перпендикулярна ВР. Значит, треугольник ВОР прямоугольный. По определению тангенса

Ответ: 6√3 (≈10,4) скажи спасибо что помог

Answer 2

Problem Analysis

We are given a circle with center O and radius 6. Point B lies on the circle, and we need to find the length of segment BR, where angle BOR is 60 degrees.

Solution

To find the length of segment BR, we can use the properties of a circle and trigonometry. Let's break down the solution into steps:

1. Draw a diagram: Draw a circle with center O and radius 6. Mark point B on the circle.

2. Find the measure of angle BOR: We are given that angle BOR is 60 degrees.

3. Find the measure of angle BOA: Since angle BOR is an inscribed angle, it is equal to half the measure of the central angle BOA. Therefore, angle BOA is 2 times angle BOR, which is 120 degrees.

4. Find the measure of angle AOB: Angle AOB is a right angle since it is formed by a radius and a tangent line at point B.

5. Use trigonometry to find the length of segment BR: We can use the sine function to find the length of segment BR. The sine of angle BOA is equal to the opposite side (BR) divided by the hypotenuse (OA). Rearranging the formula, we get BR = OA * sin(BOA).

6. Substitute the values: The radius OA is given as 6, and the angle BOA is 120 degrees. Substitute these values into the formula to find the length of segment BR.

Calculation

Let's calculate the length of segment BR using the formula BR = OA * sin(BOA):

BR = 6 * sin(120) BR ≈ 6 * 0.866 BR ≈ 5.196

Answer

The length of segment BR is approximately 5.196 units.

Please let me know if I can help you with anything else.