Question

ДАЮ 70 БАЛЛОВ!!! Хорда делит окружность на две части, градусные меры которых относятся как 4 : 8. Под какими углами видна эта хорда из точек окружности.

Answer 1

Ответ:

Пусть т.О - центр окр-сти и хорда дана АВ. Тогда по условию центральный угол АОВ (который меньше 180 градусов!) равен 4х градусов, а угол ВОА (который больше 180 градусов!) равен 5х градусов, где х - коэффициент пропорциональности. Сумма этих углов равна 4х+5х, что составляет 360 градусов. Значит 9х=360; х=40. Угол АОВ=

=4*х=4*40=160 градусов.

Искомые вписанные углы, опирающиеся на хорду АВ, равны. Их градусная мера равна половине центрального угла АОВ, т.е. 160/2=80 градусов.

Answer 2

Calculation of the Angle of the Chord

To determine the angles at which the chord is visible from points on the circumference of the circle, we need to find the angle of the chord itself. We are given that the degree measures of the two parts into which the chord divides the circle are in a ratio of 4:8.

Let's assume that the smaller angle is 4x degrees and the larger angle is 8x degrees. According to the given ratio, we have:

4x : 8x

We know that the sum of the degree measures of the two parts of the chord is 360 degrees (since the chord divides the circle into two parts). Therefore, we can set up the following equation:

4x + 8x = 360

Simplifying the equation, we get:

12x = 360

Dividing both sides of the equation by 12, we find:

x = 30

Now that we have the value of x, we can calculate the angles of the chord:

Smaller angle = 4x = 4 * 30 = 120 degrees

Larger angle = 8x = 8 * 30 = 240 degrees

Visibility of the Chord from Points on the Circumference

To determine the angles at which the chord is visible from points on the circumference of the circle, we need to consider the angles formed by the chord and the radii connecting the points on the circumference to the center of the circle.

The chord will be visible from a point on the circumference if the angle formed by the chord and the radius connecting that point to the center of the circle is equal to or greater than the angle of the chord.

In this case, the smaller angle of the chord is 120 degrees and the larger angle is 240 degrees. Therefore, the chord will be visible from points on the circumference at angles of 120 degrees or greater.

To summarize: - The chord is visible from points on the circumference at angles of 120 degrees or greater.

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