Question

Дано: коло, О — центр кола, АС і BD — діаметри, кут DOC = 30°. Знайти: кути трикутника АОВ.

Answer 1

Ответ:

 30° при вершине и два угла по 75°.

(Пояснение в приведённом ниже файле)1

Answer 2

Given Information:

We are given a circle with center O. The diameters of the circle are AC and BD. We are also given that angle DOC is 30°.

Finding the Angles of Triangle AOV:

To find the angles of triangle AOV, we need to consider the properties of a circle and the relationships between angles in a triangle.

1. Angle AOV: - Angle AOV is an inscribed angle that intercepts arc AV. - According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of its intercepted arc. - Therefore, angle AOV is half the measure of arc AV.

2. Measure of Arc AV: - Since AC and BD are diameters of the circle, they divide the circle into four equal arcs. - The measure of each of these arcs is 90°. - Arc AV is one of these arcs, so its measure is also 90°.

3. Measure of Angle AOV: - Angle AOV is half the measure of arc AV, which is 90°. - Therefore, angle AOV is 45°.

4. Angle OVA: - Angle OVA is the vertical angle to angle AOV. - Vertical angles are congruent, which means they have the same measure. - Therefore, angle OVA also measures 45°.

5. Angle AVO: - Angle AVO is the remaining angle in triangle AOV. - To find its measure, we can use the fact that the sum of the angles in a triangle is 180°. - Angle AOV and angle OVA already add up to 90°, so angle AVO must also measure 90°.

Therefore, the angles of triangle AOV are: - Angle AOV = 45° - Angle OVA = 45° - Angle AVO = 90°

Please let me know if you need any further clarification or assistance!