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varshamittal029

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

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