### Video Transcript

A circle with center π has a
diameter line segment π΄π΅. If line π΄πΆ and line π΅π· are two
tangents to the circle, what can you say about them?

To solve this, letβs go ahead and
sketch a circle. This is the circle π, with a
diameter of π΄π΅. We know that line segment π΄π΅ must
pass through the center π since it is a diameter. And then we have a line π΄πΆ. We know that we name lines by two
points that fall on that line. And because π΄πΆ is tangent to this
circle, it can only intersect the circle at point π΄. We can then sketch a line that
looks like this for π΄πΆ. The line π΄πΆ meets the diameter at
a right angle. A similar thing is true for line
segment π΅π·. We name the lines by points along
that line. And because we know itβs tangent,
it can only intersect the circle at point π΅. And so we have line π΅π·. This line also forms a right angle
with the diameter.

What weβre seeing in this image is
that line π΄πΆ and line π΅π· are parallel. The way weβve drawn it, line π΄πΆ
and line π΅π· are vertical and the diameter π΄π΅ is horizontal. But this is not the only way we
could draw the image. Letβs say we have the diameter
drawn in this way. π΄πΆ still forms a right angle with
the diameter, as does π΅π·. And again, weβll see that these two
lines are parallel. They will never intersect. If both of these images still donβt
convince you, we could do a short kind of proof.

If these lines are not parallel,
then at some point in the distance, they will intersect. And we could call that point
π. And if they intersect somewhere
really far out in the distance, they would form a triangle. And the triangle would be
π΄ππ΅. The problem is we know that angles
in a triangle must add up to 180 degrees. And since the measure of angle π΄
is 90 degrees and the measure of angle π΅ is 90 degrees, combined, they already
equal 180 degrees. This confirms that these two lines
can never intersect. They could not form a triangle and
are therefore parallel. Line π΄πΆ and line π΅π· are
parallel.