Question

К окружности с центром О проведены касательные ВА и ВС( А и С точки касания) .Найти угол АОВ если АВС =80 градусов.Зарание СПС В ответе должно получиться 50 градусов помогите пж.

Answer 1

Рассмотрим окружность.
Проведем радиусы ОА и ОС. Они равны и перпендикулярны касательным, проведенным в точку касания. Проведем ВО. 

Рассмотрим треугольники АВО и ОВС. ОВ - общая, угол А=угол С. АО=ОС. Следовательно, треугольники равны, значит равны и углы АВО и ОВС. 
Они в сумме дают угол АВО, равный 80. Значит, АВО=80:2=40 градусов.

Рассмотрим треугольник АВО - прямоугольный, следовательно, угол АОВ=90- уголАВО=90-40=50

Ответ:50

Answer 2

Finding the Angle AOV

To find the angle AOV, we need to use the given information that angle ABC is 80 degrees and that AB and AC are tangents to the circle with center O.

Let's break down the problem step by step:

1. Draw a diagram: Start by drawing a circle with center O. Then draw tangents AB and AC from point A to the circle. Label the points of intersection between the tangents and the circle as B and C, respectively. Finally, label the point of tangency between the circle and the line segment AO as D.

2. Identify relevant angles: We are given that angle ABC is 80 degrees. We need to find angle AOV.

3. Use the properties of tangents: In a circle, a tangent is perpendicular to the radius drawn to the point of tangency. Therefore, angle AOD is 90 degrees.

4. Use the properties of a straight line: The sum of the angles in a straight line is 180 degrees. Therefore, angle AOB + angle BOD = 180 degrees.

5. Calculate angle AOB: Since angle BOD is 90 degrees (as mentioned in step 3), we can subtract it from 180 degrees to find angle AOB. Thus, angle AOB = 180 degrees - angle BOD.

6. Calculate angle AOV: Since angle AOV is the exterior angle of triangle AOB, it is equal to the sum of the two remote interior angles. Therefore, angle AOV = angle AOB + angle ABC.

Now, let's calculate the angle AOV using the given information:

- Angle ABC = 80 degrees. - Angle BOD = 90 degrees (as mentioned in step 3).

Using the properties mentioned above, we can calculate the angle AOV as follows:

- Angle AOB = 180 degrees - angle BOD = 180 degrees - 90 degrees = 90 degrees. - Angle AOV = angle AOB + angle ABC = 90 degrees + 80 degrees = 170 degrees.

Therefore, the angle AOV is 170 degrees, not 50 degrees as you mentioned in your question. Please double-check the given information or provide any additional details if necessary.

Let me know if there's anything else I can help you with!