Question

АС и BD - диаметры окружности с цетром О. Угол АСВ равен 32 градуса .Найдите угол АОD.

Answer 1

диаметры окружности взаимноперпендикулярны! значит, АОД=90

наверное! 

Answer 2

Problem Analysis

We are given that AC and BD are diameters of circles with center O. The angle ASV is 32 degrees. We need to find the angle AOD.

Solution

To find the angle AOD, we need to consider the properties of angles formed by intersecting lines and circles.

From the given information, we can deduce that angle ASV is a central angle of circle O. Since AC is a diameter, angle ASV is equal to 180 degrees.

Now, let's consider the angles formed by the intersection of lines AC and BD. Angle AOC and angle BOD are both inscribed angles that intercept the same arc AD. According to the inscribed angle theorem, these angles are equal.

Therefore, angle AOC is equal to angle BOD.

Since angle AOC is equal to angle BOD, and angle AOC is 180 degrees (as it is a central angle), we can conclude that angle BOD is also 180 degrees.

Hence, the angle AOD is 180 degrees.

Answer

The angle AOD is 180 degrees.