Question

На окружности с центром в точке О отмечены точки А и В так , что угол АОВ=140 градусов . Длина меньшей дуги АВ равна 98 градусов . Найдите длину большей дуги АВ . Извините рисунок не получится добавить

Answer 1

Т. к. меньший угол АОВ=140 градусов, то больший угол АОВ=360-140=220 градусов.
т.к. длины дуг прямо пропорциональны углам, на которых они лежат, то
140/220=98/х
х=98*220/140=154

Answer 2

Problem Analysis

We are given a circle with center O and points A and B marked on the circle. The angle AOV is 140 degrees and the length of the smaller arc AB is 98 degrees. We need to find the length of the larger arc AB.

Solution

To find the length of the larger arc AB, we can subtract the length of the smaller arc AB from the total circumference of the circle.

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.

To find the radius of the circle, we can use the fact that the angle AOV is 140 degrees. The angle AOV is subtended by the arc AB, and the length of the arc AB is given as 98 degrees. The ratio of the length of an arc to the circumference of a circle is equal to the ratio of the angle subtended by the arc to the total angle of the circle.

Using this information, we can set up the following equation:

98 degrees / C = 140 degrees / 360 degrees

Simplifying the equation, we get:

98 / C = 7 / 18

Cross-multiplying, we get:

7C = 98 * 18

Simplifying further, we get:

C = (98 * 18) / 7

Now that we have the circumference of the circle, we can find the length of the larger arc AB by subtracting the length of the smaller arc AB from the circumference.

Let's calculate the length of the larger arc AB:

C - 98 degrees

Calculation

Using the given information and the equations derived above, we can calculate the length of the larger arc AB.

C = (98 * 18) / 7

Length of the larger arc AB = C - 98 degrees

Now let's calculate the values:

C = (98 * 18) / 7 = 252

Length of the larger arc AB = 252 - 98 = 154 degrees

Answer

The length of the larger arc AB is 154 degrees.