centre of a circle

sdevine89

how do u find the centre of a circle when given three points one being the orgin (0,0)?

example:a circle passes through the orgin (0,0) and the points (4,3) and (3,3) find its centre

Thomas_S_Hunterson

First find an equation for the circle and then correctly interpret the coefficients.

Thoie

http://mathforum.org/library/drmath/view/55239.html

sdevine89

do u not need the centre or radius to find the equation?

sdevine89

Thoie wrote: »

http://mathforum.org/library/drmath/view/55239.html

i saw that but when the point is (0,0) is there not another way

sdevine89

sdevine89 wrote: »

i saw that but when the point is (0,0) is there not another way

thanks for the repleys have figured it out

Thoie

What's the answer?

sdevine89

i got -7/2,1/2

LeixlipRed

You draw the circle and where you stick your compass in, that's the centre. Ooh yehhh

Thoie

sdevine89 wrote: »

i got -7/2,1/2

I got 3.5, -0.5, but there's a strong possibility I got signs mixed up along the way.

TommyGunne

Thoie wrote: »

I got 3.5, -0.5, but there's a strong possibility I got signs mixed up along the way.

Its this, not -3.5, 0.5.

Its not exactly hard to sanity check your answers. It takes two seconds to put the three points on a graph, and estimate a circle. Just doing that, without doing any equations or anything, you can tell that the x co-ordinate of the centre must be +3.5, and the y coordinate is negative and smallish, and if you take two more seconds you can just say that it is -0.5. All this without equations, just by either looking at the points in your head or drawing a few lines on paper. I never understood why people don't sanity check their answers.

hivizman

That's basically how I did it as well. If you put the points on a graph, by symmetry arguments the centre of the circle must lie on x = 3.5. Then noting that the distance between (0,0) and the line is 3.5, this implies that the centre of the circle is at 3 - 3.5, that is, -0.5. If O = (0,0), A = (3,3), B = (4,3), C = (3.5, -0.5), D = (3.5, 3) and E = (3.5,0), the triangles OEC, CAD and CBD must be congruent, and this confirms the result (note that OC, AC and BC are all radii of the circle and must therefore be equal in length).

gondorff

What's the origin of the word orgin?

Thomas_S_Hunterson

gondorff wrote: »

What's the origin of the word orgin?

Comes from Latin.

DaMonk

if you join 2 of the lines, get the midpoint of them and get the equation of line now perpendicular to the lines, there intersection is the circle centre. been awhile since leaving cert so maybe long winded.

Ishmael

Use the eqution m = (y2-y1)/(x2-x1) Find the slopes of 2 lines joining any 2 of the points together. Using (0,0), (4,3) and (0,0), (3,3) are the easiest as this simplifies the above equtation to and m = y2/x2. which gives slopes of 3/4 and 1. Get the slope perpindicular to these by inverting and multiplying by -1 which gives -4/3 and -1

Find the midpoint between the each set of 2 points.

(0,0), (4,3)

---

> (2,3/2)
(0,0), (3,3)

---

> (3/2,3/2)

Use the perpindicular slopes and the corresponding midpoint to create 2 line equations using (Y-y1) = m(X-x1)

(2,3/2), m = -4/3

---

> Y-3/2 = -4/3(X-2) ----> 8X+6Y = 25
(3/2,3/2) m = -1

---

> Y-3/2 = -1(X-3/2) ----> X+Y = 3

Solve these 2 simultaneous equations and the result is the center of the circle

8X+6Y = 25
-6X-6Y = -18

2X = 7 ---> X = 7/2
7/2+Y = 3 ----> Y = 3-7/2 = -1/2

Center of the circle is (7/2,-1/2)

pisslips

Whats the story with needing to use the equation of a circle or mid points etc.

Can you not just say, dist. of point x,y from A = dist of x,y from B and then only one of your 2 answers would make sense with respect to C. Like 2 seconds and no prior knowledge of anything really required apart from squaring and sqrt signs.