Question

Вершины треугольника АВС лежат на окружности с центром в точке О. Известно, что угол ОВС равен 55 градусов. Найдите величину угла ВАС. Буду очень благодарна за помощь.

Answer 1

ОА=ОВ=ОС т.к. это радиусы окружности

треугольники ОВС, ОВА и ОАС - равнобедренные, т.к. их боковые ребра - это радиусы окружности. Углы при их основании равны.

уголОВС=углуВСО=55градусов (по условию)

уголОВА=углуОАВ=х

уголОАС=углуОСА=y

т.к. сумма углов треугольника=180, получаем:

55+55+х+х+y+y=180

2x+2y=70

2(x+y)=70

x+y=35 градусов

 

уголВАС=х+y=35градусов.

 

Ответ: уголВАС=35градуосв.

 

(если сделать чертеж, то все легко получается)

Answer 2

Problem Analysis

We are given a triangle ABC with vertices lying on a circle with center O. We know that angle OVS is 55 degrees and we need to find the measure of angle VAS.

Solution

To find the measure of angle VAS, we can use the property that the angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at any point on the circumference of the circle.

Let's denote the measure of angle VAS as x. Since angle OVS is given as 55 degrees, we can conclude that angle OAS is also 55 degrees (since they subtend the same arc VS).

Now, we can use the property mentioned above to find the measure of angle VAS. The angle subtended by arc VS at the center O is 55 degrees. Therefore, the angle subtended by arc VS at point A is 2 times that, which is 110 degrees.

Hence, the measure of angle VAS is 110 degrees.

Conclusion

The measure of angle VAS in triangle ABC, where the vertices lie on a circle with center O and angle OVS is 55 degrees, is 110 degrees.

Please let me know if you need any further assistance.