Question

Треугольник авс вписан в окружность с центром в точке о. точки о и с лежат в одной полуплоскости относительно прямой ав. найдите угол асв если угол аов равен 67 градусов

Answer 1

Угол AOB опирается на дугу величиной 67 градусов,
Угол АСВ опирается на туже дугу и равен половине градусной меры этой дуги, т.е. 33,5

Answer 2

Triangle AVS Inscribed in a Circle

To find the angle AVS, we need to use the properties of a triangle inscribed in a circle.

Given: - Triangle AVS is inscribed in a circle with center O. - Points O, A, and S lie in the same half-plane with respect to line AV. - Angle AOV is 67 degrees.

To find angle AVS, we can use the following property:

The measure of an angle formed by a chord and a tangent at the point of contact is equal to half the measure of the intercepted arc.

In this case, line AV is a chord, and line AS is a tangent to the circle at point A. Therefore, angle AVS is equal to half the measure of the intercepted arc between points A and S.

Let's calculate the measure of angle AVS step by step:

1. The measure of intercepted arc AS is twice the measure of angle AOV, which is 67 degrees. Therefore, the measure of arc AS is 2 * 67 = 134 degrees. 2. Angle AVS is equal to half the measure of arc AS. Therefore, angle AVS = 134 / 2 = 67 degrees.

So, the measure of angle AVS is 67 degrees.

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