Question

prove that the tangents to a circle at the end points of a diameter are parallel

Answer 1

 a circle with centre 'o'
 AB is thee diameter.
PQ&RS are the tangents of the circle and point of contact is A,B end points of a diameter
R.T.P:- PQ//RS
Proof:-we know that 
       PQ PERPENDICULAR TO AB....................1
       RS PERPENDICULAR TO AB....................2
              PQ//RS (.. The lines PQ and RS are coplanar the interior on the same side of transversal are 180 degrees)
      

hope this will help you

Answer 2

Answer:

Step-by-step explanation:

consider a circle with center' O' and diameter A B

⇔       ⇔

X Y,     P Q  are tangents to  the circle

A B⊥ X Y

A B⊥P Q

(at point of contact of to the circle is 90°)

X Y ║ P Q

(in a co-planar lines alternative angles are equal)