Difference between Incenter, Circumcenter, Centroid & Orthocenter | Concept Clarification.
ฝัง
- เผยแพร่เมื่อ 5 ก.ย. 2024
- Difference between Incenter, Circumcenter, Centroid & Orthocenter | Concept Clarification | Angle Bisector | Perpendicular Bisector | Median.
In this video,we learn about Incenter, Circumcenter , Centroid & Orthocenter and Difference among them.
Incenter
In geometry, the incenter of a triangle is a triangle center, a point defined for any triangle in a way that is independent of the triangle's placement or scale. The incenter may be equivalently defined as the point where the internal angle bisectors of the triangle cross, as the point equidistant from the triangle's sides, as the junction point of the medial axis and innermost point of the grassfire transform of the triangle, and as the center point of the inscribed circle of the triangle.
Together with the centroid, circumcenter, and orthocenter, it is one of the four triangle centers known to the ancient Greeks, and the only one that does not in general lie on the Euler line. It is the first listed center, X(1), in Clark Kimberling's Encyclopedia of Triangle Centers, and the identity element of the multiplicative group of triangle centers.
Definition
The incenter lies at equal distances from the three line segments forming the sides of the triangle, and also from the three lines containing those segments. It is the only point equally distant from the line segments, but there are three more points equally distant from the lines, the excenters, which form the centers of the excircles of the given triangle. The incenter and excenters together form an orthocentric system
Circumcenter
The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersect. In other words, the point of concurrency of the bisector of the sides of a triangle is called the circumcenter. It is denoted by P(X, Y). The circumcenter is also the centre of the circumcircle of that triangle and it can be either inside or outside the triangle.
Circumcenter Formula
P(X, Y) = [(x1 sin 2A + x2 sin 2B + x3 sin 2C)/ (sin 2A + sin 2B + sin 2C), (y1 sin 2A + y2 sin 2B + y3 sin 2C)/ (sin 2A + sin 2B + sin 2C)]
Centroid
The centroid is the centre point of the object. The point in which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all the three medians. The median is a line that joins the midpoint of a side and the opposite vertex of the triangle. The centroid of the triangle separates the median in the ratio of 2: 1. It can be found by taking the average of x- coordinate points and y-coordinate points of all the vertices of the triangle.
Centroid Formula
Centroid of a triangle = ((x1+x2+x3)/3, (y1+y2+y3)/3)
Orthocenter
The orthocenter is the point where all the three altitudes of the triangle cut or intersect each other. Here, the altitude is the line drawn from the vertex of the triangle and is perpendicular to the opposite side. Since the triangle has three vertices and three sides, therefore there are three altitudes.
Orthocenter of a Triangle
The orthocenter of a triangle is the point where the perpendicular drawn from the vertices to the opposite sides of the triangle intersect each other.
• For an acute angle triangle, the orthocenter lies inside the triangle.
• For the obtuse angle triangle, the orthocenter lies outside the triangle.
• For a right triangle, the orthocenter lies on the vertex of the right angle.
Orthocenter Formula
mBE = (y-y2)/(x-x2)
mAD = (y-y1)/(x-x1)
Properties of Orthocenter
The orthocenter is the intersection point of the altitudes drawn from the vertices of the triangle to the opposite sides.
• For an acute triangle, it lies inside the triangle.
• For an obtuse triangle, it lies outside of the triangle.
• For a right-angled triangle, it lies on the vertex of the right angle.
Welcome to Nand Kishore Classes
Click at below links to download the Lectures
1. Basic Math
nandkishoreclas...
2. Shortcut Tricks
nandkishoreclas...
3. Kids Activities
nandkishoreclas...
4. Class 4
nandkishoreclas...
5. Class 5
nandkishoreclas...
6. Class 8
nandkishoreclas...
7. Class 9
nandkishoreclas...
8. Class 10th
nandkishoreclas...
9. Class 11
nandkishoreclas...
10. Class 12
nandkishoreclas...
Circumcenter: circumcenter is the point of intersection of three perpendicular bisectors of a triangle. Circumcenter is the center of the circumcircle, which is a circle passing through all three vertices of a triangle.
Incenter is the center of the circle with the circumference intersecting all three sides of the triangle.
Orthocenter is the point of intersection of the three heights of the triangle.
So clearly explained.. no one can ever forget about all of these after watching the video.. kudos to you sir and also thank you so much ☺️
Thanks
I'll forget it next week.🤣
Thankyou sir ...
Welcome
Best explanation ever in TH-cam
Thanks
Sir kasam se ek ghante me ek video mili h jisne 8 min me hi clear kr diya concept baki sab to sir 40 45 min ki vdo ti aisi hi short video banate rhiye sir thanku veryyyyyyy muchhhj👍👍👍👍👍
God bless you
Soo perfectly explained ! Tnqq so much sir !
Welcome
Thanku sir its too helpful for me🙏🙏🙏🙏
Welcome
Thank you 🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏 Sir
Most welcome
Sir you have explained very nicely
Thanks
thank sir you are a great
Thanks
Very nice 😊👏
Thanks
Thank you sir
Welcome
Fortunate to find this much crystal clear explanation....Biggggg thanks sir😊
All the best
Superbe sir jii ..,, saare doubt clear kr diye aapne toh ...jo doubt mere abhinay sir bhe clear nhe kr paye the ...
Thank you so much sir
Welcome
EXCELLENT TEACHING GURUJI ........... RADHEY RADHEY ............. 🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏👊
Radhe Radhe
Thanks sir 🙏🙏🙏
Welcome
thanks sir, yaad hogayi
Good
Thank you sir 😊
Welcome
नींद आ रही हो तो सोना नहीं है, यही समय है पढ़ने का इसे खोना नहीं है 🎯🎯🎯🎯🎯🎯🎯🎯🎯🎯🎯
धन्यवाद सर
Welcome
Thanks 🙏👍
Welcome
Very helpful video
Op explanation,🤟🤟🤟🤟
Thanks
Sir all Concepts cleared about triangle thanks to you so much sir🤩🤩
Welcome
Wah what an explanation my maths teacher is not good even I am preparing for JEE. I need this explaination for maths🙏👍👍👍👍
All the best
Best video on youtube on this concept
Thanks
I am from Pakistan 🇵🇰well explained ❤️
Bhai Pakistan Wale bhi padhte hai kya 🤣🤣 mujhe lga kewal boomb banate hai , sorry for joke🤣🤣
Clearly explained..Thank you
Welcome
Very helpful severly underrated video
Thanks for writing
@@NandKishoreClasses tomorrow is my maths board exam lol 😆
Thank u sir for clear my doubt of incentre and circumcentre
Welcome
Very beautiful explanation sir , 🌹😋
Thanks
Really a good work.thnkxx a lot
Thanks
Thx sir
Welcome
tqsm sir
Welcome
Nice explain sir
Thanks
sir thank you
Welcome
For so much helpful video
Thanks
Sir, Circumcenter of an obtuse angled triangle also lies outside of triangle
Nicely explained ☺️☺️
Thanks
Thank you sir...
Seriously helpfull 🥹
Welcome
SIR WHAT IS DIFFERENCE BETWEEN RECTILINEAR FIGURE AND POLYGON??
Super sir Allah aapko khush rakhe
Thanks
Jai shree ram 🚩
Asssalamo alikum sir please also make a video on the topic FACTORIZATION , HCF ,LCM , SIMPLIFICATION AND SQUARE ROOT
Plzzz
Allah give you path of true
JazakAllah khair
Zbrdast
RAM RAM😍
Ram Ram
Very nice video 👍👍😇
Needed this
Thank you so much for clearing all my doubts.
Welcome
Sir then circumcenter only occurs in equilateral triangle??????
👍👍👍👌
Thx
Sir ang!le bisector or median me fir difference kya h
Angles bisector angle ko equal.parts mein divide karta hai air median side ko
@@NandKishoreClasses mediansides ko divide krega to obviously angle ko bhi krega hi😐😐
2:33
Har jagah dekha mujhe yahi doubt tha circle aur triangle ke bich.. Sara dekh lia lec par kuch samjh nhinaaya tha
I want to add one more thing which was not explained...
The orthocentre may lie on any vertex if the triangle is right angled triangle
👍🙏
Thnks sir❤
Welcome
Thank You Sir
Welcome
Thank you sir❤
Welcome
Thanks sir 😊😊
Most welcome
Thanks sir
Welcome
Thank you sir 🙏🏻
Thankyou sir..
Welcome
Thank you sir 🤗
Thanks sir
Welcome