Angle α in the given problem comes to be 125°.
∠ATC =70°(given)
Suppose the center of the circle is O while both the tangents intersect at T.
As we know quadrilateral ATCO is a cyclic quadrilateral because a quadrilateral constructed by tangents, corresponding points of tangency, and the center of a circle is a cyclic quadrilateral.
What is a cyclic quadrilateral?
A quadrilateral with all its vertices on the circumference of the circle is called a cyclic quadrilateral. The sum of opposite angles is always 180° in a cyclic quadrilateral.
So, ∠AOC = 180 - ∠ATC
∠AOC = 180 - 70
∠AOC = 110°
We know that angle made by an arc at the circumference is half of the angle made by the same arc on the center.
So, ∠ABC = 110/2 = 55°.
Quadrilateral ABCD is a cyclic quadrilateral
So, α =180- ∠ABC
α =180-55
α=125°
Therefore, angle α in the given problem comes to be 125°.
To get more about the cyclic quadrilateral visit:
https://brainly.com/question/24142962
