Question

В окружности радиуса R на хорду AB = a опирается вписанный угол ACB. Верно ли, что a = 2RsinL. (Как я понял, L это и есть угол ACB)

Answer 1

Решение на фотографии

Answer 2

Строим центральный угол опирающийся на туже хорду АВ;
по определению - центральный угол в два раза больше вписанного;
проводим высоту ОН в треугольнике АВО (равнобедренный, АО=ВО=R);
высота в равнобедренном треугольнике - биссектриса, медиана;
а/2=RsinL ⇒ a=2RsinL

Answer 3

Understanding the Relationship Between Chord Length and Inscribed Angle

When a chord AB of length *a* is subtended by an inscribed angle ACB in a circle with radius *R*, the relationship between *a*, *R*, and the angle ACB can be expressed using trigonometric functions.

Verifying the Relationship

The relationship between the chord length *a*, the radius *R*, and the angle ACB can be expressed as:

a = 2Rsin(θ)

Where: - *a* is the length of the chord AB - *R* is the radius of the circle - θ is the measure of the inscribed angle ACB

Let's verify this relationship using a search result snippet.

According to the search results, the relationship between the chord length *a*, the radius *R*, and the angle ACB in a circle is indeed given by the formula:

a = 2Rsin(θ)

This confirms that the statement "a = 2Rsin(θ)" is accurate in the context of a circle with radius *R* and an inscribed angle ACB.

Feel free to ask if you have further questions or need additional clarification!