Question

К окружности с центром в точке О проведены касательная AB (B точка касания )и секущая АО .Найдите угол АОB если угол OAB=19 градусов.Ответ укажите в градусах.ПОМОГИТЕ ПЛИЗ

Answer 1

Решение приведено во вложении

Answer 2

71 градус
угол ОВА = 90 градусов
180-90-19=71

Answer 3

Problem Analysis

We are given a circle with center O. A tangent AB is drawn to the circle at point B, and a secant AO is drawn. We need to find the angle AOB, given that angle OAB is 19 degrees.

Solution

To find the angle AOB, we can use the fact that the angle between a tangent and a chord is equal to half the angle subtended by the chord at the center of the circle.

Let's denote the angle AOB as x. According to the problem, angle OAB is 19 degrees. Therefore, angle OBA is also 19 degrees, as angles OAB and OBA are equal due to the properties of an isosceles triangle.

Since angle AOB is subtended by chord AB at the center O, we can conclude that angle AOB is twice the angle OBA. Therefore, angle AOB is 2 * 19 = 38 degrees.

Hence, the angle AOB is 38 degrees.

Answer

The angle AOB is 38 degrees.