...ratio of the parts outside the circle. 321. If a tangent and secant are drawn to one point, prove that the tangent is a mean proportional between the whole secant and the part outside the circle. 322. Prove that three points fix the position of a plane. (Imagine the plane rotating...

...contained by the segments of the other. 49. If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and the part without the circle (§230). Or, If from any point without a circle two straight lines be drawn, one of which cuts the...

...proportional parts. The perpendicular to the diameter is a mean proportional between its segments. The tangent is a mean proportional between the whole secant and the exterior part of it. 51. Four lines are said to be proportional when their numerical values can form...

...sides is equi-distant from them, equal in length to half their sum, and bisects the opposite side. 3. If from a point without a circle a secant and a tangent...the whole secant and the part without the circle. 4. (a) Define a geometric locus. (b) If the base and vertical angle of a triangle be given ; find the...

...EA:EC = EC : EB; or, EA:EB = EC2. (4). Hence, if from a point w1tnout tne cIrcte a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and the part w1thout the circle. Secants of Two Circles. — In any two circles, the secants joining the extremities...

...: 0 Н, the shortest side of the other. 154 GEOMETRY. BOOK III. PROPOSITION XIII. THEOREM. 292. lf from a point without a circle a secant and a tangent...mean proportional between the whole secant and the pari without the circle. 0 С Let 0 B be a tangent and 0С a secant drawn from the point 0 to the circle...

...division point oí AB required. For AD : AB : : AB : AE, §292 (if from a point without the circumference a secant and a tangent be drawn, the tangent is a...between the whole secant and the part without the circumference). Then AD — AB : AB : : AB- AE : A E. Since AB = 2CB, Cons. and ED = 2CB, (the diameter...

...division point of AB required. For AD : AB : : AB : AE, §292 (if from a point without the eircumference a secant and a tangent be drawn, the tangent is a...proportional between the whole secant and the part vriihout the eircumference). Then AD - AB : AB : : AB - AE : A E. §265 Since AB=2CB, Cons. and ED...

...equivalent to R. For SB : SM : : SM : S С, . § 292 (if from a point without aO,a secant and a tongent be drawn, the tangent is a mean proportional between the whole secant and the part without the O). Then STI* = SBX S С; § 259 . and the difference between SB and SC is the diameter of the O, that...

...which b and B coincide; here both Ob and OB are equal to the tangent; so that the proposition will be: The tangent is a mean proportional between the whole secant and the part outside the circle. These three propositions may be expressed under one, thus: When a circle cuts several...