 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 166by George Albert Wentworth - 1899 - 256 pagesFull view - About this book
 | Robert Fowler Leighton - 1880 - 428 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 - 392 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 - 420 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 - 1893 - 680 pages
...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 - 150 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... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...two chords be drawn through a fixed point within a circle, the product of the segments of one chord is 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 APxBP^A'PXB'P.... | |
 | James Howard Gore - Geometry - 1898 - 232 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 x Bp... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...observe that BM = MC. Then Subtract the second equality from the first. Then AB* - AC* = 2 BC X MD. i,. E . D PROPOSITION XXXII. THEOREM. 378. If two chords...at 0. To prove that OM X ON = OQ X OP. Proof. Draw MP and NQ. Z a = Z a', § 289 (each being measured by $ arc PN). And Z c = Z c', § 289 (each being... | |
 | George Albert Wentworth - Geometry - 1899 - 498 pages
...+ AC* = 2 'BM* + 2 ~AM\ Subtract the second equality from the first. Then Zz? - AC* = 2 BC X MD. QE D PROPOSITION XXXII. THEOREM. 378. If two chords intersect...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. Z a = Z a', § 289 (each being measured... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
...+ Ml* = 2 KM* + 2 AM\ Subtract the second equality from the first. Then AB2 - AC* = 2 BC X MD. QED PROPOSITION XXXII. THEOREM. 378. If two chords intersect...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. Z a = Z a', § 289 (each being measured by... | |
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