...less than the distance between the centres of the given circles. 146. PROP. XLIX. To draw an arc of a circle passing through three given points (not in the same straight line"), without Jinding or using the centre of the circle. QThis is required to be done in drawing the parallels...

...Before proceeding to this problem the student should understand anothe on which, it depends, ie To draw a circle passing through three given points — not in the same straight line. Let А в and с = given points. Join А в and A с. Bisect А в and А с at right angles by straight...

...the whole line thus produced, and the produced part, shall equal the square on the part produced. 6. Describe a circle passing through three given points not in the same straight line. 7. In a given circle place a straight line equal and parallel to a given straight line not greater...

...The point D, where the bisecting lines intersect, is the centre. (Eue. ш. 1, Cor.) PROBLEM G5. — To describe a circle passing through three given points not in the same straight line. Let A, B, and С be the three points. Join AB, B С. Bisect both lines as above. From D, the point where...

...which intersect at D. This point is the centre of the circle. (Eve. III., Cor. 2.) Problem 15. — To describe a circle passing through three given points not in the same straight line. Let A, B, and C be the three points. Join AB and BC. Bisect both lines as above. From D, the point where...

...circumference were so chosen that AB and CD were parallel, this construction would fail. Why?) To draw a circle passing through three given points not in the same straight line ; in other words, To find a point equidistant from three given points. This is done as in the preceding...

...on GH. Fig. 184. The ceiitre therefore is the point of intersection of EF and GH, namely O. To draw a circle passing through three given points not in the same straight line ; in other word*, To find a point equidistant from three given points. This is done as in the preceding...