# The tangents at points A and B to the circle with center O intersect at an angle of 28 °. Find the angle ABO. Draw a segment CO.
Consider the triangle ACO.
∠ACO = ∠ACB / 2 = 28 ° / 2 = 14 ° (according to the second tangent property).
∠CAO = 90 ° (according to the first tangent property)
By the theorem on the sum of the angles of a triangle:
180 ° = ∠AOC + ∠ACO + ∠CAO
180 ° = ∠AOC + 14 ° + 90 °
∠AOC = 76 °
Consider the triangles ACO and BCO.
OC – ​​common side
AC = BC (by the second tangent property)
OA = OB (because these are the radii)
Therefore, according to the third feature, these triangles are equal.
Then ∠AOC = ∠BOC = 76 °
Consider the triangle AOB.
OA = OB (because these are the radii)
Therefore, the triangle AOB is isosceles.
Then ∠BAO = ∠ABO (by the property of an isosceles triangle).
By the theorem on the sum of the angles of a triangle:
180 ° = ∠AOB + ∠OAB + ∠ABO
180 ° = ∠AOC + ∠BOC + 2∠ABO
180 ° = 76 ° + 76 ° + 2∠ABO
28 ° = 2∠ABO
∠ABO = 14 ° Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.