 | Robert Fowler Leighton - 1880 - 428 σελίδες
...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 - 1886 - 392 σελίδες
...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 - 1890 - 420 σελίδες
...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 σελίδες
...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 - 1894 - 150 σελίδες
...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 - 1894 - 400 σελίδες
...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 - 1898 - 232 σελίδες
...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 - 1899 - 272 σελίδες
...AC* = 2 ~BM i + 2 AM2 Subtract the second equality from the first. Then Iff - AC* = 2 BC X MD. Q . E . D PROPOSITION XXXII. THEOREM. 378. If two chords...at 0. To prove that OM X ON= OQ X OP. Proof. Draw HP and NQ. Z a = Z a', § 289 (each being measured by ± arc PN). And Z c = Z c', § 289 (each being... | |
 | George Albert Wentworth - 1899 - 272 σελίδες
...AI? + AC*=2'BM* + 2AM*. Subtract the second equality from the first. Then ~AB* - AC* = 2 BC X MD. QED PROPOSITION XXXII. THEOREM. 378. If two chords intersect...two chords MN and PQ intersect at 0. To prove that OH X ON= OQ X OP. Proof. Draw HP and NQ. Z a = Z a', § 289 (each being measured by $ arc PN). And... | |
 | Alan Sanders - 1901 - 260 σελίδες
...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 AEC... | |
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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. 
