Question

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

Answer 1

Answer:

No, the tangents cannot intersect  outside the circle. When tangents intersect outside a circle, the measure of the angle they form is one half the difference of the intercepted arcs. Since the tangents are at the endpoints of the same diameter, both intercepted arcs would have to measure 180 degrees. This means the angle would have a measure of one half times the difference of 180 and 180, which is 0. An angle with a zero degree measure could not intersect a circle on opposite sides.

Step-by-step explanation:

That's the sample text

Answer 2

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