...and QB tangents of the circle O; prove RQ minus RA plus QB. 3. If two chords in a circle intersect, the product of the segments of one chord is equal to the product of the segments of the other chord. 4. The side of an equilateral triangle is a. Find the area. 5. In a circle whose radius is 50...

...(2), we have AC* + 1BC* = 2 AD* + 2 CD*. Subtracting (2) from (1), PROPOSITION XXXI. THEOREM. 280. If any two chords be drawn through a fixed point within...equal to the product of the segments of the other. Let AJl and A'B' be any two chords passing through the fixed point P within the circle ABB'. To prove...

...first class mathematical preparation for the study of Boyle's Law. Of this class, is the following: "If two chords be drawn through a fixed point within a...equal to the product of the segments of the other." The data could be arranged as follows : ab Pass various lines through P and measure accurately the...

...ratio of the corresponding values of the other, they are said to be reciprocally j»'oportinnal. Thus, if any two chords be drawn through a fixed point within a circle, their segments are reciprocally proportional. PROPOSITION XXXII. THEOREM. 282. If through a fixed point...

...equal sides of an isosceles triangle as a diameter passes through the middle point of the base. 3. If two chords be drawn through a fixed point within a circle, the product of the segments of one chord equals the product of the segments of the other. 4. The radius of a circle is 10 ; inscribe within...

...equal sides of an isosceles triangle as a diameter passes through the middle point of the base. 3. If two chords be drawn through a fixed point within a circle, the product of the segments of one chord equals the product of the segments of the other. 4. The radius of a circle is 10 ; inscribe within...

...in the same ratio, they are said to be reciprocally proportional. Then, the theorem may be written, If any two chords be drawn through a fixed point within a circle, their segments are reciprocally proportional. t * PROP. XXIX. THEOREM. 282. If through a fixed point...

...2AD> + 2 CD2. Subtracting (2) from (1), we have (§ 278) (§ 277) (1) (2) PROP. XXVIII. THEOREM. 280. If any two chords be drawn through a fixed point within...equal to the product of the segments of the other. Given AB and A'B' any two chords passing through fixed point P within O AA'B. To Prove AP x BP = A'P...

...values of the other, they are said to be reciprocally proportional. Then, the theorem may be written, If any two chords be drawn through a fixed point within a circle, their segments are reciprocally proportional. PROP. XXIX. THEOREM. 282. If through a fixed point without...

...III. 18. Hence, A EBD is similar to A ECA. Th. 20. Whence, AE : DE =• EC : EB. Def. 5. COR. — Tlie product of the segments of one chord is equal to the product of the segments of the other. For from the preceding proportion we have AE x EB = DE x EC. PROPOSITION XXXII. — THEOREM. If from...