Q.circle geometry (1 Viewer)

[marsenal]

ABCD is a cyclic quadrilateral such that AC is a diameter, DC produced meets AB produced at S, and BC produced meets AD at T.
Prove that ST is parrallel to the tangent at A.
Also it was has been established that BSTD is a cyclic quadrilateral with ST as diameter.

 

[Constip8edSkunk]

let EAF be an interval on the tangent at A so that

Angle EAB = BCA(angle between tangent and chord equal to angle subtended by chord blah blahblah)

Angle BCA=BDA(anglesubtended by same chord)

angle BDA=BST(angle subtended ny the same chord{of circle BSTD})

Therfor
Angle BST=EAB

therefor
EA || ST (alt. angles equal; transversal SA)