Question

У колі з центром у точці О проведено хорду АВ і діаметр ВС .Знайдіть кути трикутника АОС,якщо кут АОВ=146 градусів.Допоможіть будь ласка.Пліз

Answer 1

Нет возможности рисунок нарисовать.

Угол АОС смежный с углом АОВ, поэтому равен 180°-146°=34°

, треугольник АОС равнобедренный. т.к. ОС=ОА как радиусы, значит, два других угла А и С в треугольнике АОС равны по

(180°-34°)/2=146°/2=73°

Answer 2

Problem Analysis

We are given a circle with center O and a chord AB, as well as diameter BC. We need to find the angles of triangle AOC, given that angle AOB is 146 degrees.

Solution

To find the angles of triangle AOC, we can use the properties of circles and triangles.

First, let's analyze the given information. We know that angle AOB is 146 degrees. Since AB is a chord of the circle, angle AOB is half of the central angle subtended by the same arc. Therefore, the central angle subtended by arc AB is 2 * 146 = 292 degrees.

Now, let's consider triangle AOC. We know that angle AOC is a central angle subtended by arc AC. Since AC is a diameter of the circle, angle AOC is a right angle (90 degrees).

To find angle OAC, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, angle OAC = 180 - angle AOC - angle ACO.

Let's calculate angle OAC:

angle OAC = 180 - angle AOC - angle ACO = 180 - 90 - angle ACO = 90 - angle ACO

To find angle ACO, we can use the fact that it is half of the central angle subtended by arc AC. Therefore, angle ACO = 0.5 * (360 - angle ACB).

Now, let's calculate angle ACO:

angle ACO = 0.5 * (360 - angle ACB) = 0.5 * (360 - 292) = 0.5 * 68 = 34 degrees

Finally, let's calculate angle OAC:

angle OAC = 90 - angle ACO = 90 - 34 = 56 degrees

Therefore, the angles of triangle AOC are: - angle AOC = 90 degrees - angle OAC = 56 degrees - angle OCA = 34 degrees

Note: The solution assumes that the given information is correct and that the circle is a standard Euclidean circle.

Answer

The angles of triangle AOC are: - angle AOC = 90 degrees - angle OAC = 56 degrees - angle OCA = 34 degrees

I hope this helps! Let me know if you have any further questions.