How to Find Circumcenter Given 3 Vertices (Algebraically)

Learn how to find the circumcenter given 3 vertices of a triangle algebraically in this math video tutorial by Mario's Math Tutoring. We discuss what the circumcenter is and how to find it. This particular problem involves using the midpoint formula, slope formula, perpendicular slope, and point slope form of a line.
0:09 What is the Circumcenter?
0:55 Significance and applications of the circumcenter
1:26 Find the midpoint of the side
2:17 Find the Slope of the side
2:45 Find the perpendicular slope
3:07 Use Point Slope Form of a Line to write equation of perpendicular bisector.
3:58 Find the Midpoint of a second side of the triangle
4:31 Find the slope of the second side
4:53 Find the Perpendicular slope of the second side
5:00 Write the equation of the perpendicular bisector
5:44 Using substitution to solve the system of equations and find the circumcenter
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[@manarm5503]

who else here because school doesn't teach this to them correctly

[@avanowak8169]

i’m on quarantine right now and my teacher got fired and they expect me to take a test via zoom tomorrow i’m gonna die 💀

[@alinasarkissian2025]

i just didtn take online class seriously but also that

[@DutDutGoose]

my teacher literally gave us the worksheets and told us to figure it out in breakout rooms

[@displacedicon7643]

yes...

[@KarenLopez-tp7bt]

@@alicezhou6328 half my class is failing

[@superiorpanda6449]

The way I learned more here in less then 10 minutes then I did sitting at my laptop for hours

[@joshuawu2585]

IKR so helpful

[@a_dash2]

Aren't you watching this on your laptop too?

[@Lily_Walker_Einstein710]

I was sitting for 2 hours in front of my laptop finding the answers and then finally got the concept.

[@superiorpanda6449]

@@a_dash2 Yeah, back then I was complaining about my online teacher's method of teaching. Looking back on it he did try and I'm sure he was thrown into a loop too with the pandemic and all.

[@leventunlimited2812]

savvas?

[@VivaanBhaskar]

This man is single handedly holding my grade up!

[@Duck.Tape.]

ikr :)

[@emmabeelner5712]

i learn more from this man's channel than my high school geometry teacher

[@angelartamesia2]

Your explanation was way easier than my teachers... or I just took the time to study, thank you!

[@stubs322]

Bro my math class has been confused about this because our teacher doesn’t know how to teach it. This guy just taught to me in seven minutes💀

[@geraldillo]

Great explanation once again, thanks!

[@MariosMathTutoring]

Glad you liked the video!

[@Albetyrizztein]

This man teaches me stuff in half of the time my teacher can, and he does it better

[@dicesonz3039]

Doing honors geometry over the summer and tbh all your videos have been a god send, since the pace of my class is just a bit to fast to really understand anything.

[@tejmurthy4852]

Why can't you be my Math teacher?

[@aerosoI]

pretty sure he is

[@dokage112]

this guy taught me more in 10 mins than my teacher did in 6-7 class periods

[@boredduck]

its odd how I can be confused for an entire year then come here and suddenly know everything I honestly do not know why I always wait to turn to this channel when I am about to fail a final. If I used this channel more I could be doing calc by now

[@mrwilliam109]

mr pak has sent me to this place

[@kevinmedina4503]

This was so helpful thank you

[@justinshimonkarborani4581]

thank you man, my teacher gave us the question without even showing us how to do do it

[@rajroy44]

A straight forward way to solve for the circumcentre (a.b) is to solve for a.b from(a-x1)^2+(b~y1)^2=(a~x2)^2+(b~y2)^2=(a~x3}^2+{b~y3)^2. (xi,yi) being the vertices I =1,2:3 you will get two linear equations in a and b .solving them is easy

[@Pretz.exe_has_stopped_working]

I'm in 7th grade, an when I first learned this, I was totally confused on how to solve this, since my teacher explained it so vaguely, and basically said, "You're on you're own now, kid!" This explanation was amazing, and saved my grades. Tysm

[@MariosMathTutoring]

Glad it helped!

[@leventunlimited2812]

mario, youre amazing

[@lindali2169]

Thank you so much, I was literally dying before this

[@Baljitkaur-xr6sb]

Best video ever!!!!

[@sin817]

Thanks mister, im in 8th grade and i have a test tomorrow., This helped.

[@devpatel8453]

Nice Explanation,
Try tutorials for Higher secondary maths also : )

[@laurenh5504]

you are saving my life right now

[@pranavr.8716]

This really helped! Thanks!:)

[@enbaoliang6938]

bru me trying to get how to do this in 1 hr

[@pranavr.8716]

@@enbaoliang6938 actually though

[@venicegoulden3399]

THANK YOU!!!! with my test in 2 days I still couldn't understand this until now

[@himeshsawai]

i'm watching from india and you are teaching great

[@amanrai937]

It can also be done by distance formula since all the vertices are at equal distance from it so we can easily get 2 equations fir two variables.
But great alternative though

[@datotokmajeshvili6415]

amazing vid. thank you Mario!

[@dev0907]

This just saved me from my quiz

[@kamil_raza89]

Keep working......u r doing great

[@MariosMathTutoring]

Thanks Kamil! Glad you like my videos!

[@jenniferwagner580]

Thank you for this video and explanation. In my Saxon Geometry book it doesn't explain it either, but why don't you also find the midpoint (and then slope and perpendicular) of line AC? Or maybe I should ask, does it matter which 2 midpoints (and slope and perpendicular) you choose to find?

[@samrudhnair9185]

well, it doesn't matter which two midpoints you choose to find. As for your first question, the point of intersection of two lines will not differ if you add a third line, meaning you only need to find the point of intersection of two perpendicular bisectors.

[@sakuralee2552]

This is sooooooo helpful!

[@danielcarrazco524]

thank you for your explanation

[@MariosMathTutoring]

You are welcome!

[@b.ravitejarajkumar1301]

Sir how to find circumcenter when in 3d geometry where z axis is included

[@jollitea2149]

Thanks for this video it helped me witih my homework

[@EdmundoBlanco]

yo your the goat for this

[@SSDIY-tz1pq]

You’re very helpful thank you !

[@math-matictv9406]

Thank you sir

[@MariosMathTutoring]

You’re welcome!

[@awkwardgaming9865]

how about getting out two perpendicular equation going through the middle point of two arms of the triangle and solving them?

[@JumpdeArt]

Thanks very helpful!

[@radhakumawat5314]

Thanks

[@kanushkapatolia504]

thanks bestie ❤

[@trungnguyenlethien8526]

in that formula , what if m = (yA - yB)/(xA - xB) when xA - xB or yA - yB equal 0?

[@jimkau9979]

Thank you so much

[@Arisxgon]

What do you do if your slope is dividing by zero

[@theboringchannel8125]

Thank you sir 🙏

[@joyfunnahar4843]

Thank you sir❤

[@thor4568]

Thank you!

[@BababooeyTheThird]

thanks dude

[@luckyduckygames810]

U saved me for my finals

[@allisonashley8023]

THANK YOU!!!

[@hydroxic648]

tysm I really appreciate it

[@sandip6333]

Love from India

[@hekati7889]

You taught me how to do this in 7 minutes, and school failed me after an hour of trying

[@rosiemoonbeam9550]

Can you PLEASE do this for GEOMETRY? PLEASE?!!

[@gurmeetschani]

can't you convert the fraction into decimals and then go from there?

[@kingnothing4848]

Lmao I was looking for help on a problem and these are literally the EXACT POINTS

[@srinathortho]

can't we simply find a point equidistant from all 3 vertices using distance formula

[@tsunayoshisawada8062]

If an edge is purely vertical, you end up with -(1/0) as a slope, which obviously simply don't work. Is there a method that could work for any A, B and C?

[@dbdmthepulse]

what are you talking about? a slope of 0/1 is a horizontal line

[@tsunayoshisawada8062]

yeah, and if you divide by 0, mathematics tend to not like that@@dbdmthepulse

[@dbdmthepulse]

@@tsunayoshisawada8062 1/0 is just a vertical line, the perpendicular of that would be 0/1 which is just a horizontal line. This method does work with any value as long as you keep in mind the perpendicular to a purely vertical line, is a purely horizontal line.

[@tsunayoshisawada8062]

So... it doesn't work for every value since one of them is a special case...@@dbdmthepulse

[@ashakirdak4897]

Can we solve that by circle formula :(x-h)²+(y-k)²=R² ?

[@chalammvs5674]

Yes asha we can but if you don't know about slopes but it's a long process and we can use it because circumcentre is equidistance from vertices hope you doing well 👍🙏

[@wickedpuma6331]

Is this in a level?

[@TGKBPlayzz]

Ur legend for true

[@ankurrajput1713]

Any Indian here 🙄❤️

[@nikhleshwarshrivastava6883]

Yeah ११th std student

[@meena_g_2226]

Same bhai

[@ali-ht5oe]

how about the center of circle in tringle

[@MariosMathTutoring]

Incenter…find where the 3 angle bisectors intersect.

[@ali-ht5oe]

@@MariosMathTutoring the question is find the center of a circle incenter like you said and we have only the a .b .c the adges of the tringle
and thanks for replay

[@syedhashir2970]

Thanks for the amazing lecture
Jeff Bezos
(just kidding 😁)

[@Meauseum]

At 4:43 he did something wrong, the B vertices must be X1, Y1 and the C Vertices must be X2 Y2, when he replaced them both, the entirety of this is false.

[@kabirs5833]

Baldi basics
Bro gonna chase me around with a ruler

[@joshuakim7845]

Mr. Pak sent me to this place

[@vivekpatil5464]

Want such teacher in our school

[@josephjoy7714]

Jeff bezos is teaching math

[@SpectrumBSlikesubnotis6707]

Isn't it supposed to be -1/4 for M (perpendicular) BC and for the fraction simplification 4 has to multiply with 3. Other than that thank you, I was struggling with this in my Geometry class and this made me understand

[@arianasosa3336]

I have the attention span of a 1 month old baby so I had to rewatch this so many times 😔

[@vishvjani3933]

Why side AC SLOPE AND MID POINT YOU HAD NOT FIND

[@Imagqne]

could you only find two lines?

[@MariosMathTutoring]

Yes

[@purplewind4015]

I tried lime AC and I got a different answer

[@bobby_carmins]

1 -2

[@enbaoliang6938]

yesser

[@fred-tk9kg]

I got lost sadly

[@weiene8990]

thavnmk

[@aswanthkrishna4445]

Jeff Bezos

[@nicolasfilet2716]

This doesnt help at all talk slower and write down the equations used and how they matter

[@CoolcookieAud]

I hate geometry I want to quit school cuz of it

[@danielpark4279]

mr pak has sent me to this place