Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 350 off


May i know what is the formula for orthocentre and circumcentre?

5 years ago


Answers : (1)


Dear Apurva

Although it's easier just to find the equation of the perpendicular bisectors of two sides (mid point formula, gradient formula inverted with sign changed, then use point gradient formula), and solve these simultaneous equations. That's what  did using points (x1, y1), (x2, y2), (x3, y3).
Calculate the determinants
D = | x1 .. x2 .. x3 |
,.,,, | y1 .. y2 .. y3 |
..... | 1 ..... 1 .... 1 |

D1 = same as above, except that the x values are squared
D2 = same as above, except that the y values are squared
Then the circumcentre is given by
x = [D1 - (y1 - y2)(y2 - y3)(y3 - y1)] / 2D
y = [D2 - (x1 - x2)(x2 - x3)(x3 - x1)] / 2D

For the orthocentre, it's not very hard to find the equation of the line through A perpendicular to BC, the line through B perpendicular to AC, and solve these simultaneous equations. I haven't yet worked out a formula for the result of that. Will edit this if I do. Email me if you'd like an example.

OK, I have a formula for the orthocentre. Calculate the determinants
D3 = | x2x3 .. x3x1 .. x1x2 |
....... | .. y1 ..... y2 ........y3 |
....... | ..1 ......... 1 ........ 1 .|
D4 the same but with y2y3 etc in the top row. Then
x = -(D3 + D4)/D

Now calculate D5 and D6, the same as these but with x replacing y in the middle row. Then
y = (D5 + D6)/D

All the best.




Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar  respectively : Click here to download the toolbar..

5 years ago

Post Your Answer

Other Related Questions on Analytical Geometry

find the equation of the circle whose centre is (-3,1) and which cuts off an intercept of length 6 from the line 2x-5y+16=0
Step 1 : General Equation of circle is given by – x^2 + y^2 + 2gx + 2fy + c = 0 whose Centre = (-g, -f) and Radius^2 = g^2 + f^2 + c Step 2: given Centre = -3, 1 therefroe g = 3 and f...
Vijay Mukati 3 months ago
A circle passes through (2,1) and x+2y=1 is tangent to it at (3,-1). Find its equation
find the perpendicular distance from cenetr of circle to the given tangent. m = |x1 + 2y1 – 1|/|root(x1^2 + y1^2)| and equate it to root((x1-3)^2 + (y1+1)^2) = m {from distance formulae}...
Vikas TU 3 months ago
Find the equation of the circle having center in the first quadrant, touching the x – axis, having a common tangent y = √3x +4 with the circle x^2 + y^2 + 4x + 4y + 4 = 0 such that the...
Let the equation of the circle having center in the first quadrant, be x^2 + y^2 + 2gx + 2fy + c = 0......................(1) touching the x – axis, .i.e y = 0 put it in eqn. (1), and and...
Vikas TU 3 months ago
if 1+sin a =9 cos a then 5(1-cos a)= sin a 2 sin a 4 isn a tan a
1+sin a =9 cos a Divide by cosa to the whole eqn., seca + tana = 9 seca = 9 – tana sq. both sides, sec^2a = 81 + tan^2a – 18tana 1 + tan^2a = 81 – 18tana + tan^2a tan^2a got cancel. 80 =...
Vikas TU 2 months ago
Find the sum upto n terms. 1/3 + 2/21 + 3/91 + ..........
-> 1/1*3 + 2/3*7 + 3/7*13 ... For eveey denom. first terms Let a= 1+ 3 + 7... Nth term for it will be n²-n+1 For every denom. second terms Let b= 3 + 7 + 13.... Nth term for it will be...
2017 years ago
I have confusion between undefined and infinite. For example,tan 90 degrees is undefined or infinite?Please clarify my doubt.
Tha 90 is undefined because tan90 have different values when we approach it from different side of 90 as shown. Since there right hand and left hand limits of tanx at x= 90 are not same,...
Ajay 2 months ago
View all Questions »

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 3,750 off

Get extra R 350 off

More Questions On Analytical Geometry

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details