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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[superiorpanda]

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

[manarm]

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

[angelartamesia]

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

[VivaanBhaskar]

This man is single handedly holding my grade up!

[emmabeelner]

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

[geraldillo]

Great explanation once again, thanks!

[stubs]

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💀

[dicesonz]

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.

[amanrai]

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

[Albetyrizztein]

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

[jenniferwagner]

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?

[rajroy]

A straight forward way to solve for the circumcentre (a.b) is to solve for a.b (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

[justinshimonkarborani]

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

[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

[b.ravitejarajkumar]

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

[himeshsawai]

i'm watching from india and you are teaching great

[dokage]

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

[awkwardgaming]

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

[devpatel]

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