Question

Show that the tangents drawn to a circle at the extremities of its diameter are parallel to each other

Answer 1

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Answer 2

Answer:

According to the question,

The tangents are drawn from the extremities of the diameter.

Now we know that the tangents drawn from any point on the circumference of the circle are perpendicular to the line drawn from the center of the circle to the point.

So,

In the figure we can see that 'l' and 'm' are the tangents from the point A and B.

As the line OA is perpendicular to 'l' also OB is perpendicular to 'm' and AB is a straight line that is a diameter, AB.

So,

As the Sum of the Internal angles on the same side is = 90° + 90° = 180°.

Or,

Alternate interior angles of the line are also equal to each other and is equal to 90 degrees.

Therefore, we can say that the lines are parallel to each other.

Hence, Proved.