Two tangents each intersect a circle at opposite endpoints of the same diameter. is it possible for the two tangents to intersect each other outside the circle? explain why or why not

Both the tangents AB and CD are parallel to each other. Therefore, it is not possible that the two tangents to intersect each other outside the circle.

Given :

Two tangents each intersect a circle at opposite endpoints of the same diameter.

A straight line that touches the circle at a single point is known as the tangent. This tangent is perpendicular to the diameter of the circle at the point of tengency.

So, let EF be the diameter of the circle whose center is O. In order to determine the two tangents intersect each other outside the circle or not, first consider two tangents AB and CD that touch the circle at points E and F respectively.

So, according to the definition of the tangent, tangent AB is perpendicular to the diameter EF at point E and also tangent CD is perpendicular to the diameter FE at point F.

So, both the tangents AB and CD are parallel to each other. Therefore, it is not possible that the two tangents to intersect each other outside the circle.

For more information, refer to the link given below:

link

It is impossible these two tangents intersect each other outside the circle because they parallel to each other

Step-by-step explanation:

* Lets explain the tangent to circle

- A tangent to a circle is a straight line which touches the circle at only

 one point.

- This point is called the point of tangency.

- The tangent to a circle is perpendicular to the radius at the point of

 tangency

- The tangent to a circle is perpendicular to the diameter at one of its

 endpoints and this end point is the point of tangency

* Now lets solve the problem

- If we have a circle with center O

- AB is a diameter of circle O

- CD is a tangent to circle O at point A

- EF is a tangent to circle O at point B

∵ AB is a diameter

∵ CD is a tangent to circle O at A

∵ The tangent and the diameter are perpendicular to each other at the

  point of tangency

∴ CD ⊥ AB at point A

∵ EF is a tangent to circle O at B

∵ The tangent and the diameter are perpendicular to each other at the

  point of tangency

∴ EF ⊥ AB at point B

- There is a fact if two lines perpendicular to the same line then these

 two lines are parallel

∵ CD ⊥ AB and EF ⊥ AB

∴ CD // EF

- We prove a fact in the circle, if two tangents drawn from the endpoints

 of a diameter, then these two tangents are parallel to each other

∵ CD and EF are parallel

∴ CD and EF never intersect each other

∵ The two tangents each intersect a circle at opposite endpoints of

  the same diameter are parallel

∴ It is impossible these two tangents intersect each other outside

 the circle because they parallel to each other