Question

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

Answer 1

Answer:

Refer attached images for your answer.

Answer 2

Given : Circle , Diameter  , Tangents

To Find : prove that the tangents to a circle c at the end points to a diameter are parallel​

Solution:

Let say AB is the diameter

and O is the center

PQ  and ST are tangent lines touching circle at  R and U respectively

Draw a line XY parallel to PQ   passing through O

∠ORP  = 90°  ( tangent)

∠ORP + ∠ROX  =  180°   Interior angles are supplementary. ( adds up to 180°)

∠ROX = 90°

∠ROX  +  ∠UOX =  180°   ( linear pair )

=> ∠UOX =  90°

    ∠OUS  = 90°  ( tangent)

=> ∠UOX  +      ∠OUS  = 180°

=> XY ||   ST

PQ || XY

and XY II ST

=> PQ II ST

Hence  tangents to a circle c at the end points to a diameter are parallel

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