Tangent to a Circle Video Lecture - Class 10

hey there everyone and welcome back to
mashup math my name is Anthony and thank
you for joining me on this mini lesson
just go ahead and check it out hey there
everyone thanks again for joining me on
this lesson where we are going to
explore the relationship between circles
and tangent lines so let's start with
the question what is a tangent line to a
circle haha cool so let's take a look at
a circle with a Center at Point P
and let's also imagine another point on
the circle and we'll call that point
T
a tangent line to a circle is a line
that intersects the circle at exactly
one point in this case our point
T
now if we construct a line that connects
that center point P with that point T on
the outside of the circle we would be
constructing a radius and we can call
that line R so PT is a radius of circle
P and if we look at the angle created by
the radius and the tangent line we
should see that this appears to be a
right angle measuring 90 degrees and
this is the case with tangent lines and
circles and we can say that a tangent
line is perpendicular to a circles
radius so we if we add another point on
the tangent line point J you can
conclude that angle P TJ has a measure
of 90 degrees and this perpendicular
relationship between a circles radius
and a tangent line applies to every
circle in any occasion so the key
concepts to understand here is that a
tangent line intersects a circle at
exactly one point and that a tangent
line and the radius it intersects are
perpendicular cut cool so now let's go
ahead and apply our understanding of
tangent lines and circles to a practice
problem in this case we have line
segment UT and line segment UV both
being tangent to circle oh and we're
looking to find the value of x shown on
the diagram so notice that lines UT and
UV are line segments however they are
still tangent to circle o which means
that they will still hold the same
properties of tangent lines even though
they are not infinite lines and we
should also note that we know that angle
o has a value of 121 degrees and that
angle U is the value of x that we are
looking to find
now we know that UT and UV are tangent
lines to circle o and we know that a
tangent line is perpendicular to the
radius it intersects so we can conclude
that angles T and V are right angles and
have measures of 90 degrees
we should also notice that we are
dealing with a quadrilateral here in
this diagram and we know that the sum of
the interior angles in any quadrilateral
is always equal to 360 degrees so if we
take these four angle measures and add
them together their sum will equal 360
and we can use this fact to find the
value of x 121 plus 90 plus 90 Plus
whatever X is is going to equal 360 and
now we can just use some basic algebra
to isolate the value of x and find out
its value in this case adding the three
angles that we do know gives a value of
301 subtracting 301 from 360
results in 59 which is the value of X
and we can conclude that angle U is 59
degrees so now that you understand the
properties of tangent lines and circles
and have got some more experience
applying those relationships to practice
problems like this one you can continue
to apply your skills and understanding
to future problems so thank you again
for stopping by everyone and I'll catch
you soon haha cool all right so that's
it for this lesson thank you again for
stopping by I hope you found it helpful
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next time bye