– English Lyrics

Lyrics & Translation

[English]

special thanks to Katrina EG for posting

this amazing geometry question on X the

end result is literally going to shock

you we have this big semicircle and

inside it we have two small semicircles

of diameter two and three and this

yellow one is tangent to the red

semicircle our job is to find the

diameter of the big

semicircle so can you solve it at first

glance if we pull this down here it

looks like the bigger diameter is simply

the sum of both of these diameters so

the answer we are looking for is five or

it will be approximately five but now

how to find out the exact value of this

diameter for that we will break this

diameter into smaller sections this this

and this one this piece right here is

the same as the radius of this

semicircle and thus it will be of length

one now to find the length of this part

first draw this radius and then join

both of these radi together this will be

1.5 and this will be 1 + 1.5 or

2.5 now we will use Pythagoras Theorem

to find the length of this part we can

do the math to find it and I have done

it for you in case you might want to

check but we have an easier method to

figure it out if we multiply the length

of both of these sides by two we get the

this as three and this is five and thus

we know that it is a three four five

Pythagorean triplets and therefore this

will be four or if we divide it by two

we get this side length as two excellent

next we will find the length of this

part and we are done let us label this

as y now here comes the magic this is

what I found the most intelligent way to

solve for this part complete this circle

now make a rectangle around it so the

length of this side of the rectangle

will be the same as the diameter of this

circle which will be three now extend

this line to the vertex of this

rectangle awesome now consider these two

triangles this angle is the same for

both these triangles and also since both

of these lines are parallel this angle

is also the same for both of them and

hence both these triangles are s similar

therefore this side which is 2 over this

side which is 1.5 equals this side which

is y + 2 over this side which is 3 cross

multiply to get this this becomes 6 over

1.5 or 4 = y + 2 or Y = 2 woohoo now is

the time for our final answer drums

rolling in and and it is 1 + 2 + 2 or 5

which is exactly the same as we

predicted at the beginning of this video

when we looked at this problem

visually isn't this cool if you liked

this video then please don't forget to

share it with your friends and support

this channel by joining our community

and becoming a member so good

[Music]