Question

В окруж­но­сти с цен­тром O AC и BD — диа­мет­ры. Угол ACB равен 26°. Най­ди­те угол AOD. Ответ дайте в гра­ду­сах.

Answer 1

Problem Analysis

We are given a diagram with points A, B, C, and D. The angle ACB is given as 26°, and we need to find the angle AOD.

Solution

To find the angle AOD, we can use the fact that the sum of the angles in a quadrilateral is 360°. Since A, O, C, and D form a quadrilateral, we can find the angle AOD by subtracting the sum of the other three angles from 360°.

Let's calculate the other three angles:

1. Angle ACB is given as 26°. 2. Angle ACD is the same as angle ACB because AC and BD are diameters, and the angle subtended by a diameter at any point on the circumference is always 90°. Therefore, angle ACD is also 26°. 3. Angle BCD is the same as angle AOD because they are opposite angles formed by two intersecting lines. Therefore, angle BCD is also 26°.

Now, we can calculate the angle AOD:

Angle AOD = 360° - (Angle ACB + Angle ACD + Angle BCD)

Substituting the values:

Angle AOD = 360° - (26° + 26° + 26°)

Simplifying:

Angle AOD = 360° - 78°

Calculating:

Angle AOD = 282°

Therefore, the angle AOD is 282°.

Answer

The angle AOD is 282°.