Question

На рисунке МК-диаметр окружности. Найдите длину хорды МС, если угол М равен 30 градусов, а длина окружности равна 24П

Answer 1

Треугольник МСК - прямоугольный, угол С=90, т.к опирается на диаметр, КМ - гипотенуза = 2 х радиус, радиус = длина окружности / 2 х пи = 24 х пи / 2 х пи =12, диаметр = 24

хорда СМ = КМ х cos30 = 24 х корень3/2 = 12 х корень3

Answer 2

РЕШЕНИЕ ВО ВЛОЖЕНИИ!!!!!!!!!!!!!!!!

Answer 3

Calculation of Chord Length MC

To find the length of chord MC, we need to use the given information that angle M is 30 degrees and the length of the circumference is 24П.

Let's analyze the given information and solve the problem step by step.

1. We know that the angle at the center of a circle is twice the angle at the circumference that intercepts the same arc. In this case, angle M is 30 degrees, so angle MAC is 60 degrees.

2. Since angle MAC is 60 degrees, angle MOC (the central angle) is also 60 degrees because they intercept the same arc.

3. The length of the circumference is given as 24П. The formula for the circumference of a circle is C = 2Пr, where r is the radius. Since the length of the circumference is 24П, we can equate it to 2Пr and solve for r.

24П = 2Пr Dividing both sides by 2П, we get: r = 12

4. Now that we have the radius, we can find the length of chord MC. In a circle, the length of a chord can be calculated using the formula:

Length of chord = 2 * radius * sin(angle/2)

Substituting the values, we get: Length of chord MC = 2 * 12 * sin(60/2) = 24 * sin(30) = 24 * 0.5 = 12

Therefore, the length of chord MC is 12.

Please let me know if you need any further assistance.