Point O-center of the circle, AD-tangent to this circle, angle BOA = 120. Find the BAD value in degrees.

| February 4, 2021 | education

If a drawing is not given to the problem, then we will consider two solutions.
Option 1.
Point B is located on a circle on the other side of point A where point D.
Consider a triangle AOB – isosceles (ОА = ОВ – radii). The angle at the top is known, we find the angle at the bottom:
∠ OAB = (180 ° – ∠ BOA) / 2 = 30 °.
Tangent AD is perpendicular to radius OA, ∠ OAD = 90 °.
Find the BAD angle:
∠ BAD = 90 ° – ∠ ОАВ = 90 ° – 30 ° = 60 °.
Answer: The BAD angle is 60 °.
Option 2
Point B is located on a circle on the other side of point A.
Consider a triangle AOB – isosceles (ОА = ОВ – radii). The angle at the top is known, we find the angle at the bottom:
∠ OAB = (180 ° – ∠ BOA) / 2 = 30 °.
Tangent AD is perpendicular to radius OA, ∠ OAD = 90 °.
Find the BAD angle:
∠ BAD = 90 ° + ∠ ОАВ = 90 ° + 30 ° = 120 °.
Answer: The BAD angle is 120 °.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.