Table of Contents
A circle that passes through 3 points
When three different points, P (X
obtain the center coordinates O (X, Y) and the radius R of the circle that
passes through these points.
To satisfy the above conditions, the
distances between P, Q, S and O
should be equal. as they are the
radius of the same circle. Therefore,
PO = QO = SO = R
Using the Pythagorean theorem,
2
= ( X
– X )
PO
1
= ( X
– X )
2
QO
2
= ( X
– X )
2
SO
3
then
2
(X
+Y
1
X =
2
(X
+Y
1
Y =
R = (X – X
To enhance both readability and writability of the program, intermediate
variables G, H, I, J, K and M are used.
The above equations reduce to
GM – HK
X =
2 (IM – JK)
Press b 2 1 0 to open a window for creating a NEW program.
1.
Type CIRCLE for the title then press e.
2.
• A NEW program called 'CIRCLE' will be created.
3.
Enter the program as follows.
Program code
Print"ENTER COORDS
G=X≥Œ+Y≥Œ-X√Œ-Y√Œ
* Calculate intermediate
values.
2
+ ( Y
– Y )
2
= R
1
+ ( Y
– Y )
2
2
= R
2
+ ( Y
– Y )
2
2
= R
3
2
2
2
-X
-Y
)(Y
–Y
1
2
2
2
2{(X
–X
)(Y
–Y
1
2
2
2
2
2
-X
-Y
)(X
–X
1
2
2
2
2{(Y
–Y
)(X
–X
1
2
2
2
2
)
+ (Y – Y
)
1
1
Y =
i 1 @ a ENTER s COORDS
; e
; G ; = @ v X1 e
e A + @ v d Y1 e
e A - @ v d d X2
e e A - @ v d
d d Y2 e e A e
Chapter 8: Application Examples
, Y
), Q (X
, Y
1
1
2
2
P (X
, Y
1
–Y
Y
1
2
2
2
2
2
) – (X
+Y
-X
3
2
2
3
) – (X
–X
)(Y
–Y
3
2
3
1
2
2
) – (X
+Y
-X
3
2
2
3
) – (Y
–Y
)(X
–X
3
2
3
1
GJ – HI
2 (KJ – MI)
Key operations
), S (X
, Y
) are given,
3
3
R
)
1
R
O (X, Y)
X
–X
1
R
2
2
-Y
)(Y
–Y
)
3
1
2
------ 1
)}
2
2
2
-Y
)(X
–X
)
3
1
2
------ 2
)}
2
------ 3
Q (X
, Y
)
2
2
S (X
, Y
)
3
3
95
Table of Contents
