DE is parallel to ST as ∠ EAT = ∠ AED which are alternate interior angles.
∠TAC = ∠ABC (The angle between the chord and the tangent is equal to the angle in the alternate segment)
Since, EDCB is a cyclic quadrilateral,
∠CBD + ∠CED = 180 ----- I
- ∠CED + ∠AED = 180 -----II
----------------------------------------------------
∠ CBD = ∠AED
Also, ∠ CBD = ∠ EAT( A is tangent to the circle)
So, ∠ EAT = ∠ AED ( Alternate interior angle)
So, DE || ST
Therefore, DE is parallel to ST as ∠ EAT = ∠ AED which are alternate interior angles.
Learn more about alternate interior angles here:
https://brainly.com/question/24839702
#SPJ9
