Geometry

[woeful plover]

hmmm

tell me all rectangles conditions

let him answer -_-

[vale nexus]

oh mb

[woeful plover]

xD

u figured out eh?

[vale nexus]

i thought u didnt knew xD

[long vault]

If all angles are right angles or the perpendicular lines are parallel

[vale nexus]

ayo what

[long vault]

What?

[vale nexus]

how can perpendicular lines be parallel

[long vault]

I meant opposite

Mb

[vale nexus]

im assuming the single line, double lines means those sides are equal

is that right?

[long vault]

Yeah

[woeful plover]

hm

anything yk abt similar triangles then

[long vault]

A little bit but I didn't find them helpful

[woeful plover]

@long vault the angles are same.

yk both are isoceles as per diagaram...

[long vault]

Yeah the thing is I thought for some reason that you can't call the diagonals same because of some reason

[woeful plover]

listen to me carefully

see this diagram..

[long vault]

Yeah

[woeful plover]

if i have the angles of triangle a as 1 and 2

and angles of triangle of b as 3 and 4

then

what the value of the green angle

[long vault]

1 +3

[woeful plover]

NICE

and we know 1=2 and 3=4

@long vault cuz its isosceles

[long vault]

Yes

[woeful plover]

now if the red is 2 and blue is 4

and

[long vault]

Wasn't red 2?

[woeful plover]

smth cuz

its

same

1=2

OH

my bad then

@long vault u can see a black angle

right

and a blue and red angle

[long vault]

Yes

[woeful plover]

hmmmm

they all lie on a line

i wonder what they add up to.. do yk? @long vault

[long vault]

180

[woeful plover]

nice

and

[long vault]

Red and blue added are 90

[woeful plover]

now..

[woeful plover]

u cant say that yet..

[long vault]

The black one is a right angle

That is a given

[woeful plover]

wasnt given..

Breh

is it so

then

u got 90

u can prove its parallel

and gotta prove sides are

equal

[woeful plover]

now 2+4=1+3...

use that fact

as 1+3= green

[long vault]

How though

[woeful plover]

(the beauty is perpendicular lines to a common line are all parallel!)

think about it

[long vault]

That line is only perpendicular to where is intercepted that line and not with that opposite one

[woeful plover]

wait

u got that green is = 90 degree right

[long vault]

Yeah

[woeful plover]

u can prove yellow too is 90

[long vault]

But the line in the middle isn't parralel to the side at least it is not given yet

[woeful plover]

ill tell you

wait

[long vault]

Ok

[woeful plover]

u got yellow angle is 90 too right

like similar stuff

[long vault]

Ye

[vale nexus]

i got it

mathematically

[woeful plover]

nice

[woeful plover]

now

they both are on a common line

[long vault]

Yep

[woeful plover]

@long vault right?

[vale nexus]

if u want it solved from variables then feel free to ask

[woeful plover]

and they are perpendicular to a common line

[long vault]

I will try on my own but can I DM you if I can't?

[vale nexus]

sure just ask i will make it

[long vault]

Yes

[woeful plover]

if a line has 2 or more lines perpendicular to it, the lines perpendicular to the line are parallel

and this can be proved

[long vault]

Makes sense

[woeful plover]

corresponding angles---> 90 degrees.

[long vault]

I really am greatful @woeful plover but gtg now I will be back in 2 and a half hours

I really have to go

[woeful plover]

tada, you got it as a rectangle. just prove parallel sides are equal

[woeful plover]

np bro gotchu

i suggest you to try RMO (if u indian) or IMO etc,

[long vault]

But that doesn't necessarily have to be right for example this

[woeful plover]

they dont have a common line, infact a common tangent.

[long vault]

What is the difference between this one and the other

[woeful plover]

each point on a circle has one and only one tangent and one possible position such that the radius even touches the tangent

[woeful plover]

hmm

say the diameter is a line

right?

[long vault]

Yeah

[woeful plover]

its a line segment. not a line.

now 2 tangents are drawn, they are perpendicular so they are parallel

However, when u shift one part of the radius at some angle the tangent that is perpendicular to the initial raidus isnt parallel

cuz

both the radius aint a line no more.

[long vault]

I don't completely understand because say you take the initial problem and take the straight line on the left as the diameter and the two lines on the top and bottom as the tangents drawn in the pic would it be the same thing

[long vault]

And this one definitely isn't a rectangle

[woeful plover]

hmm

its night time in my country i gotta go sleep

but

wait

@long vault in this these 2 diagrams in which does the diameter form a line

[long vault]

Frist

[woeful plover]

mhm

so what did i say earlier

common line thing state it

[long vault]

Ah ok gn then we can talk bout it tomorrow

[woeful plover]

ill make u understand then ill go sleep.

[long vault]

If you say so

[woeful plover]

.

[long vault]

And what if it is a common line

[woeful plover]

just state it xD

no overthinking alr? just focus..

[long vault]

I don't get what exactly you are trying to tell me if you imagine it is a common line then the statement that is a line exists on which two other line are perpendicular then the corresponding line are right angles wouldnt make sense

[long vault]

.

[woeful plover]

no imagining.. there actually exists a common line.

[woeful plover]

wait

ill explain

[long vault]

Ok

[woeful plover]

@long vault say there is this common line and has some lines intersecting it with angles A1 A2 A3.. call the lines as 1 2 3 and angles as A1 A2 A3.

now if Line 1 2 3 must be parallel what is the relation between angle A1 A2 A3? @long vault

[long vault]

90

[woeful plover]

nope

A1=A2=A3..

[long vault]

they are the some

[woeful plover]

this must be angle.

[long vault]

same

[woeful plover]

yea

correct

now

A1=A2=A3 are same then if they are 90.. @long vault are they still parallel?

[long vault]

yes?

[woeful plover]

thats all.

[long vault]

but in my pic the middle one isnt 90 degrees

only the ones one the side

the one in the middle can be anything

[woeful plover]

thats cuz it isnt a line

middle what

like

oh

the middle raidus?

[long vault]

yeah

[woeful plover]

radius*

thats cuz

it isnt a diameter..

like

it doesnt form 180 with the initial radius

i said a common line must be present: a line has 180 degree

does this radius and the other radius have 180 degree between them @long vault ?

[long vault]

which of the there exacly

three

[woeful plover]

does this have 180 degree

[long vault]

no

[woeful plover]

then how can it be aline?

it isnt.

[long vault]

the diameter is the line

there are 3 tangents

[woeful plover]

yep

ok restate ur doubt

[long vault]

wait a sec i will draw it

[woeful plover]

u say this red coloured thing's tangent isnt parallel right

[long vault]

The diameter is a and e f and g are the radii

The yellow line you drew would be e and g combined

[woeful plover]

ok.. u have confused urself my friend.

[woeful plover]

oh thats yellow? im colourblinf mb

[woeful plover]

nuh uh!

e and g is perpendicular

u shdnt confuse 2 diagrams. geometry's first rule.

[long vault]

but why are e and g perendicular

[woeful plover]

according to initial q

u said the red coloured angle is 90 is 90 degrees

[long vault]

yea

[woeful plover]

can i explain tmr

[long vault]

but not the one on the other side

[woeful plover]

i gotta go sleep

[long vault]

sure

thanks anyways

[woeful plover]

@vale nexus oi if possible help the boy

[woeful plover]

ill tell ya one thing tho, you smart as hell, go for IMO smth.

which standard u in byw

[long vault]

you mean clas

s

?

[woeful plover]

yes

[long vault]

i am in 11💀

[woeful plover]

US?

or smth like tha

[long vault]

germany

[woeful plover]

cuz me and u same class

[long vault]

crazy

[woeful plover]

tf ?

all from india bro

dw

ill teach u tmr

gn.

[long vault]

ok thanks

gn

but wait

where from india?

[woeful plover]

@vale nexus help the guy if possible

[woeful plover]

somewhere.. doesnt matter xD

idw to get doxxed.

[long vault]

yeah mb shiuldnt have asked

[vale nexus]

@long vault

sorry i had an exam so i was available

[long vault]

But 1 and 2 don't necessarily have to be equal 40 plus 50 is also 90

[vale nexus]

the sides i colored red are equal

cuz u have marked a single line on all 3 of them

[long vault]

True

For example this is obv not a rectangle

I kinda have the feeling that it's not possible

[woeful plover]

is M midpoint?

i need the full problem.

[woeful plover]

I taught him that and stuff hes confused on why perpendicular lines to a common line are not paralle

[long vault]

M is the mid pint and C D and E are point where the circles touche the edges of the big semi circle

Same goes for the two points on MP

[woeful plover]

i c

the best way to do is to first start.

draw a rough and recognize what all u hv been given and what all u can do.

[woeful plover]

xD

its not all about angles.. Open for hint or dont ----> ||(why would i see a common tangent to both the circles.. huh wait a minute thats somehow related to the semicircle, and also i have already told u perp lines are parallel when they have a common line)||

i also forgot circle properties but if u want it here:

||MP=MB=AM. see circle kB MP and MB are equal tangents... and radius perpenticular stuff u can draw and try ||

[long vault]

How can mp and mb help me there

I dont see any correlation

[woeful plover]

MP and MB are radius of semicircle..

be calm and try

[long vault]

Ah I missunderstood I thought you meant those lines somehow prove the right angle or something

[long vault]

On it

[woeful plover]

nah. chill