Question

prove that the tangents drawn from the end of the diameter of a circle are always parallel

Answer 1

Given:- CD and EF are the tangents at the end points A and B of the diameter AB of a circle center O.
To prove :- CD parallel to EF
Proof :- CD is the tangent to the circle at the point A .
Therefore,
CD perpendicular to OA= Angle OAD = 90 degree.
EF is the tangent to the circle at the point B.
Therefore,
EF perpendicular to OB = Angle OBE= 90 degree.= Angle ABE = 90 degree.
Thus,
Angle BAD = Angle ABE ( each equal to 90)
But these are alternate interior Angle.
Therefore,
CD parallel EF..

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Answer 2

Draw the diameter vertically
And tangents horizontally then 2angles would be 90 nd alternate
Hence 2tangents are parralel