Question

The plane x+2y+z=6 cuts x,y and z axes at A,B and C.Find x coordinate of circumcentre of ∆ABC

Answer 1

you can find the three coordinates.. then use that to find the circumcentre

Answer 2

Really! do you know the formula for that?
For circumcentre part

Answer 3

no i don't know any formula but there are two methods..

Answer 4

One method i definitely tried.Bt ended up nowhere.

Answer 5

which one ? intersection of perpendicular bisectors?

Answer 6

The way in which we equate the radius of the circle knowing the three vertices and a centre assumed to be (a,b,c)

Answer 7

oh okay, but the shorter method is you can find angle A and the solve

Answer 8

Other way is finding or tho center but i don't know that too.

Answer 9

there is one formula that involves sin2A.. have you heard of it?

Answer 10

but the perpendicular bisectors intersection will surely work

Answer 11

We can't apply it here ,i think so (sin2A formula) becoz this is a 3-D figure.

Answer 12

I m just now getting how can you apply perpendicular bisectors also becoz we never know the equation of lines here.
Do we?

Answer 13

I m just now getting how can you apply perpendicular bisectors also becoz we never know the equation of lines here.
Do we?

Answer 14

\[(6,0,0), (0, 3, 0), (0, 0, 6)\]By symmetry, the \(x\) and \(z\) coordinates of the center will be the same. So assume the center to be \((a, b, a)\).\[(a-6)^2 + b^2 + a^2 = a^2 + (b-6)^2 + a^2 \]\[\Rightarrow -6(2a-6) = 6(2b-6)\]\[\Rightarrow 3 - a = b-3\]\[\Rightarrow a + b = 6\]\[(a-6)^2 + (a-6)^2+a^2 = a^2+(a-3)^2 + a^2 \]Finally, \(a = 7/2\) and \(b = 5/2\).

The circumcenter is \((7/2, 5/2, 7/2)\)

Answer 15

we can find the eqs of line using the coordinates

Answer 16

If you want to know this method (per. bis.) here is a link:
https://www.youtube.com/watch?v=kwooTzS01PA

Answer 17

How you did this?
a^2+(b-6)^2+a^2 in the first equation
I got this a^2+(b-3)^2+a^2

Answer 18

@parthkohli i literally don't know how did you came up with values of a and b
I just got an equation which is 9=4a-2b

Answer 19

Even i didn't understand.. @parthkohli can explain from the symmetry part?

Answer 20

Did you get the same equation as i wrote above.
Further as far as i see,he has done a typo in that.

Answer 21

Even i didn't understand.. @parthkohli can explain from the symmetry part?