By
Viewed
38,771
Please choose the correct answer for each question below:
Questions: 0/60
Correct: 0
Translate:
I really love this type of geometry
questions we have a rectangle and we
have a circle which is touching this
rectangle at this vertex now we draw a
straight line starting from this vertex
of the rectangle like this which Cuts
The Circle at two different points one
is this Vertex or this point of contact
and the other is this point now this is
the center of this circle and this is
the point of contact of this circle with
the ground it is given that these three
points are cinear which means they lie
on a straight line the diagonal of this
rectangle is 32 units and the length of
this cord is equal to 18 units our job
is to find the area of this circle so
can you find it okay now consider this
circle and these two lines since this is
the point of contact of this circle with
the ground therefore this line is going
to be the tangent to this circle right
also this line is a secant line of this
circle so we can use the second tangent
theorem which means if we have this
circle and an external Point P somewhere
here now draw a tangent line which
touches the circle at Point T and then
we draw a secant line which Cuts The
Circle at points A and B like this so
the theorem says that the length of the
segment PT s equals the length of the
segment p a times the length of the
segment PB so here if we label the
length of this piece as L then we get l
s equals length of this diagonal or 32 *
length of this entire second or 32 + 18
or 50 units so l s = 1600 which gives L
= 40 units
amazing next let us draw this line which
connects all these three cinear
points now consider this triangle what
will be the value of this angle yes you
are right it will be a right angle
because this will be a diameter as it
passes through the center of the circle
and we know that the diameter is always
perpendicular to the tangent line let us
label the length of this diameter as 2 R
where R is the radius of this circle now
we can use the Pythagoras Theorem to get
40 sare + 2
r² equals this hypotenuse or 50 squ so 4
r² = 2500 -600 or 900 so r² = 900 over 4
or
225 now the area is equal to PK * r² or
225 pi and that's it this is our final
answer wasn't this an amazing problem so
good
[Music]
Related Songs