If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other. Plane Geometry - Page 183by John Wesley Young, Albert John Schwartz - 1915 - 223 pagesFull view - About this book
| 1880 - 412 pages
...the quadrilateral. 6. If two chords intersect within the circle, the product of the segments of the **one is equal to the product of the segments of the other.** Prove. What does this proposition become when the chords are replaced by secants intersecting without... | |
| Webster Wells - Geometry - 1886 - 371 pages
...C'D'' (3) (3) 137 PROPOSITION XXIX. THEOREM. 291. If any two chords are drawn through a fixed point **in a circle, the product of the segments of one is...equal to the product of the segments of the other.** Let A~B and A'B' be any two chords of the circle ABB', passing through the point P. To prove that Ap^BP... | |
| Edward Albert Bowser - Geometry - 1890 - 393 pages
...Proposition 29. Theorem. 335. If two chords cut each other in a circle, the product of the segments of the **one is equal to the product of the segments of the other.** Hyp. Let the chords AB, CD cut at P. To prove AP X BP = CP x DP. Proof. Join AD and BC. In the AS APD,... | |
| Rutgers University. College of Agriculture - Technology & Engineering - 1893
...the intercepted arcs. 4. If two chords cut each other in a circle, the product of the segments of the **one is equal to the product of the segments of the other.** 5. The area of a triangle is equal to half the product of its base and altitude. 6. The areas of si... | |
| George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 138 pages
...interior angles not adjacent ? 2. The sum of the angles of a triangle is equal to two right angles. 4. **If two chords intersect in a circle the product of...equal to the product of the segments of the other.** 5. Two triangles having an angle of one equal to an angle of the other are to each other as the product... | |
| James Howard Gore - Geometry - 1898 - 210 pages
...adjacent to that side. PROPOSITION XVIII. THEOREM. 229. If any tiuo chords are drawn through a fixed point **in a circle, the product of the segments of one is...equal to the product of the segments of the other.** Let AB and A'B' be any two chords of the circle ABB' passing through the point P. To prove that Ap... | |
| George Albert Wentworth - Geometry, Plane - 1899 - 256 pages
...second equality from the first. Then Iff - AC* = 2 BC X MD. Q . E . D PROPOSITION XXXII. THEOREM. 378. **If two chords intersect in a circle, the product of...equal to the product of the segments of the other.** Let any two chords MN and PQ intersect at 0. To prove that OM X ON= OQ X OP. Proof. Draw HP and NQ.... | |
| George Albert Wentworth - Geometry - 1899 - 473 pages
...the second equality from the first. Then Zz? - AC* = 2 BC X MD. QE D PROPOSITION XXXII. THEOREM. 378. **If two chords intersect in a circle, the product of...equal to the product of the segments of the other.** Let any two chords MN and PQ intersect at O. To prove that OM X ON = OQ X OP. Proof. Draw MP and NQ.... | |
| Alan Sanders - Geometry, Plane - 1901 - 247 pages
...is equal to the square of the radius. PROPOSITION XXII. THEOREM 528. // two chords intersect within **a circle, the product of the segments of one is equal to the product of the segments of the other.** Let the chords AB and CD intersect at E. To Prove AE . EB = CE . ED. Proof. Draw AC and DB. Prove A... | |
| Universities and colleges - 1917
...are equal, respectively, to the three sides of the other. 2. a) Prove: If two chords intersect within **a circle, the product of the segments of one is equal to the product of the segments of the other.** b) A and B are two points on a railway curve which is an arc of a circle. If the length of the chord... | |
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