...EF parallel to BC. [§ 347.] PLANE GEOMETRY — BOOK III 747 The tangent and the perpendicular drawn from any point in the circumference of a circle to a diameter divide the diameter harmonically. 748 If two circles are tangent internally, all chords of the larger...

...inscribed in a semicircle is a right angle (§ 194), it follows that : If a perpendicular be drawn from any point in the circumference of a circle to a diameter, 1. The perpendicular is a mean proportional between the segments of the diameter. 2. The chord joining...

...inscribed in a semicircle is a right angle (§ 194), it follows that : If a perpendicular be drawn from any point in the circumference of a circle to a diameter, 1. The perpendicular is a mean proportional between the segments of the diameter. 2. The chord joining...

...hypotenuse divides a right triangle into two similar triangles. 383. COB. 3. If a perpendicular be drawn from any point in the circumference of a circle to a diameter, II. The chord from that point to either extremity of the diameter is the mean proportional between...

...triangles as in Fig. 51? 16. In a circle the perpendicular from any point in the circumference to the diameter is a mean proportional between the two segments of the diameter. In Fig. 52 DC is perpendicular to AB and meets AB in C which is 4 units from A and 16 units from B....

...chord be (r, 0) and (6, c). 42. Prove analytically that the length of a perpendicular from any point on the circumference of a circle to a diameter, is a mean proportional between the segments into which it divides the diameter. 43. Prove that the length of the tangent from the point...