Question

Хорда окружности равна 12см и стягивает дугу градусной меры 60 градусов найдите диаметр окружности

Answer 1

Пусть  АВ - данная хорда, АВ=12 см. Соединим концы хорды с центром окружности: ОА и ОВ .
∠АОВ - центральный, равен дуге, на которую опирается: ∠АОВ=60°.
ОА=ОВ= АВ= 12 см. 
Диаметр окружности равен дум радиусам, 2·12= 24 см.
Ответ: 24 см.

Answer 2

Finding the Diameter of a Circle

To find the diameter of a circle, we can use the formula:

Diameter = 2 * Radius

In this case, we are given the length of a chord and the degree measure of the corresponding arc. Let's solve the problem step by step.

Given: - Length of the chord = 12 cm - Degree measure of the arc = 60 degrees

To find the diameter, we need to find the radius first. We can use the following formula to find the radius:

Radius = (Length of the chord) / (2 * sin(angle/2))

Here, the angle is given in degrees, so we need to convert it to radians before using the formula. The conversion formula is:

radians = (degrees * pi) / 180

Let's calculate the radius:

Step 1: Convert the angle from degrees to radians: - Angle in radians = (60 * pi) / 180 = pi/3 radians

Step 2: Calculate the radius using the formula: - Radius = (12 cm) / (2 * sin(pi/3)) - Radius = (12 cm) / (2 * √3/2) - Radius = (12 cm) / (√3) - Radius = 4√3 cm

Step 3: Calculate the diameter using the formula: - Diameter = 2 * Radius - Diameter = 2 * 4√3 cm - Diameter = 8√3 cm

Therefore, the diameter of the circle is 8√3 cm.