Page:The Elements of Euclid for the Use of Schools and Colleges - 1872.djvu/328

304 15. To describe a circle which shall pass through a given point and touch two given circles.

Let A be the centre of the smaller circle and B the centre of the larger circle; and let E be the given point.

Draw a straight line touching the former circle at G and the latter at D, and meeting the straight line AB, produced through A, at T. Join TE and divide it at F so that the rectangle TE, TF may be equal to the rectangle TC, TD. Then describe a circle to pass through E and F and touch either of the given circles (10); this shall be the required circle.