– English Lyrics

Lyrics & Translation

[English]

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]

Key Vocabulary

Vocabulary	Meanings
rectangle /ˈrɛk.tæŋ.ɡəl/ B1	noun - a four-sided polygon with four right angles
circle /ˈsɜːr.kəl/ A1	noun - a round shape with every point on its edge equidistant from the center
vertex /ˈvɜːr.tɛks/ B1	noun - a corner or meeting point of lines or edges (as in a polygon or graph)
line /laɪn/ A1	noun - a straight one-dimensional figure extending infinitely in both directions
tangent /ˈtæn.dʒənt/ B2	noun - a line that touches a circle at exactly one point adjective - touching a circle at one point; related to a tangent
secant /ˈsiː.kənt/ B2	noun - a line that intersects a circle at two points
center /ˈsen.tər/ B1	noun - the middle point of a circle or shape
diagonal /daɪˈæɡ.ə.nəl/ B2	noun - a line joining opposite corners of a polygon
diameter /daɪˈæm.ɪ.tər/ B2	noun - a line through the center of a circle touching the circle at two points
radius /ˈreɪ.di.əs/ B2	noun - a line segment from the center to any point on the circle
area /ˈeər.i.ə/ B1	noun - the measure of the size of a surface
triangle /ˈtraɪ.æŋ.ɡəl/ A2	noun - a polygon with three sides
theorem /ˈθiː.rəm/ B2	noun - a proven statement that is typically used as a building block in math
Pythagoras /pɪˈθæɡ.ə.rəs/ C1	noun - the ancient Greek mathematician known for the Pythagorean theorem
perpendicular /ˌpɜː.pənˈdɪ.kjə.lər/ B2	adjective - forming a right angle; vertical to another line
right /raɪt/ A2	adjective - correct; just; also used for a 90-degree angle (angle right) adjective - pertaining to a 90-degree angle
contact /ˈkɒn.tækt/ B1	noun - the state of touching or being in touch
length /leŋkθ/ A2	noun - the measurement of something from end to end
point /pɔɪnt/ A1	noun - a particular position or place
draw /drɔː/ A1	verb - to produce lines, shapes, or pictures by moving a pencil or pen