Sharp EL-5230, EL-5250 Circle that passes through 3 points, Using the Pythagorean theorem

Chapter 8: Application Examples

A circle that passes through 3 points

When three different points, P (X1, Y1), Q (X2, Y2), S (X3, Y3) are given, 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						Q (X2, Y2)
distances between P, Q, S and O		P (X1, Y1)			R
should be equal. as they are the		Y1–Y	R
radius of the same circle. Therefore,					O (X, Y)
			X1–X
PO = QO = SO = R
				R
Using the Pythagorean theorem,
PO2 = (X1 – X)2 + (Y1 – Y)2 = R2						S (X3, Y3)
QO2 = (X2 – X)2 + (Y2 – Y)2 = R2
SO2 = (X3 – X)2 + (Y3 – Y)2 = R2
then	(X12+Y12-X22-Y22)(Y2–Y3) – (X22+Y22-X32-Y32)(Y1–Y2)
X =						------ 1
	2{(X1–X2)(Y2–Y3) – (X2–X3)(Y1–Y2)}
Y =	(X12+Y12-X22-Y22)(X2–X3) – (X22+Y22-X32-Y32)(X1–X2)					------ 2
	2{(Y1–Y2)(X2–X3) – (Y2–Y3)(X1–X2)}
R = (X – X1)2 + (Y – Y1)2					------ 3

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

X =	GM – HK	Y =	GJ – HI
	2 (IM – JK)		2 (KJ – MI)

1.Press b 210to open a window for creating a NEW program.

2.Type CIRCLE for the title then press e.

•A NEW program called ‘CIRCLE’ will be created.

3.Enter the program as follows.

Program code	Key operations
Print”ENTER COORDS	i 1 @ a ENTER s COORDS
	; e
G=X≥Œ+Y≥Œ-X√Œ-Y√Œ	; G ; = @ v X1 e
* Calculate intermediate	e A + @ v d Y1 e
values.	e A - @ v d d X2
	e e A - @ v d
	d d Y2 e e A e

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