22. If a variable line, whose extremities rest on the circumferences of two given concentric circles, subtend a right angle at any fixed point, the locus of its middle point is a circle.
BOOK III.
THEORY OF THE CIRCLE
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DEFINITIONS.
i. Equal circles are those whose radii are equal.
This is a theorem, and not a definition. For if two circles have equal radii, they are evidently congruent figures, and therefore equal. From this way of proving this theorem Props. xxvi.–xxix. follow as immediate inferences.
ii. A chord of a circle is the line joining two points in its circumference.
If the chord be produced both ways, the whole line is called a secant, and each of the parts into which a secant divides the circumference is called an arc—the greater the major conjugate arc, and the lesser the minor conjugate arc.—Newcomb.
iii. A right line is said to touch a circle when it meets the circle, and, being produced both ways, does not cut it; the line is called a tangent to the circle, and the point where it touches it the point of contact.