– English Lyrics

Lyrics & Translation

[English]

this is an amazing question because in

this single question we will be using

four different theorems like cord chord

power theorem perpendicular bis sector

of a chord phases theorem and Pythagoras

Theorem we have a circle now draw this

chord its length is 13 units then draw

this line which is perpendicular to this

chord its length is six units then draw

another line which is perpendicular to

this line its length is 18 units our job

is to find the radius of this circle so

can you solve it okay in order to solve

this problem let us draw a line which

will be parallel to this line like this

now this is 13 and this is 18 units so

what will be the length of this piece

yes you are right it will be 18 -3 or 5

units right now let us draw this line

and complete this chord and let us label

the length of this piece as H now there

is a theorem called the perpendicular

bis sector of a chord theorem which

states that a line drawn from the center

of a circle to a cord which is

perpendicular to the cord will always

BCT it or cut the cord into two equal

halves so let us draw this perpendicular

bis sector line from the center of this

circle using the theorem both of them

will be 13 / 2 now since these two lines

are parallel and this is a right angle

therefore this length will be equal to

this and thus it will be 13 / 2

similarly this will also be

13/2 right now again using the

perpendicular bis sector of a chord

theorem on this chord both these pieces

will be of equal length therefore we get

13 / 2 + H will be equal to this will be

13 /2 + 5 therefore H equal 5 let us

clear things up noise now here starts

the real magic we can now use a theorem

called the chord chord power theorem

imagine two lines crossing inside a

circle making four pieces like this let

us label the sides as a b c and d the

theorem says that if you multiply the

lengths of the two parts of one chord or

a * B then it will always be equal to

the same multiplication for the other

chord or C * D now let us draw a line

like this what will be the length of

this piece of the chord label it as M

look at these four parts of the chord we

can use the chord chord power theorem

here to get this times this or 18 * 5 =

this * this or 6 * m therefore we get M

= 90 over 6 or 15 units so what will be

the length of this cord it will be 15 +

6 or 21 units again let us clear things

up and remove the unnecessary lines

great now let us connect these two

points with each other see clearly I

have made this line pass through the

center of this circle do you know why

here comes another theorem called

thales's theorem which states that if a

triangle is formed inside a circle with

one of its sides as the diameter of the

circle then the angle opposite to the

diameter is always a right angle or 90°

which means it will pass through the

center of this circle now if we label

the radius of this circle as R then this

diameter will be of length 2 * R right

so finally we can use our favorite right

triangle theorem here to get 2 r² =

s + 21 s therefore 4 r² = 169 +

441 or

610 thus r² = 610 / 4 which will be

152.5 and therefore R equals the square

root of this which is approximately

12.35 units and that's it this is our

final answer answer if you enjoyed this

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[Music]

Key Vocabulary

Vocabulary	Meanings
circle /ˈsɜːr.kəl/ A1	noun - a round shape consisting of all points equidistant from the center
draw /drɔː/ A1	verb - to create a picture or diagram with a pen or pencil
chord /kɔːrd/ B1	noun - a line segment joining two points on a curve
perpendicular /ˌpɜːr.pənˈdɪk.jə.lər/ B2	adjective - at an angle of 90 degrees to a horizontal line or surface
theorem /ˈθiː.ə.rəm/ B2	noun - a statement proven based on logical arguments
radius /ˈreɪ.di.əs/ B1	noun - the distance from the center to any point on the edge of a circle
parallel /ˈpær.ə.leɪl/ B1	adjective - never meeting, always the same distance apart
length /leŋkθ/ A2	noun - the measurement of how long something is
center /ˈsen.tər/ A1	noun - the middle point of a circle or sphere
triangle /ˈtraɪ.æŋ.ɡəl/ A1	noun - a shape with three sides and three angles
diameter /daɪˈæm.ɪ.tər/ B1	noun - a straight line passing through the center of a circle
angle /æŋ.ɡəl/ A2	noun - the space between two lines or surfaces at the point where they meet
square /skweər/ A1	noun - a shape with four equal sides and four right angles verb - to multiply a number by itself
multiply /ˈmʌl.tɪ.plaɪ/ A2	verb - to add a number to itself a certain number of times
approximately /əˈprɒk.sɪ.mət.li/ B2	adverb - almost exact but not completely accurate