Answer:
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
