 | William Chauvenet - 1871 - 380 σελίδες
...of the opposite sides. (III. 64) and (Ex. 23.) 141. In any quadrilateral ABCD inscribed in a circle, the product of the diagonals is equal to the sum of the products of the opposite sides ; that is, AC.DB = AD.BC + AB.DC. (Make the angle DAE = BAC, and prove that AD.BC =AC.DE, and AB.DC... | |
 | Edward Olney - 1872 - 102 σελίδες
...joining the centres of the diagonals. 677. In any quadrilateral which may be inscribed in a circle, the product of the diagonals is equal to the sum of the products of the opposite sides. 6Y8. In any triangle the rectangle of two sides is equivalent to the rectangle of the perpendicular... | |
 | Edward Olney - 1872 - 96 σελίδες
...FIG. 381. squares of the diagonals. 252 677. In any quadrilateral which may be inscribed in a circle, the product of the diagonals is equal to the sum of the products of the opposite sides. 678. In any triangle the rectangle of two sides is equivalent to the rectangle of the perpendicular... | |
 | William Chauvenet - 1872 - 382 σελίδες
...of the opposite sides. (III. 64) and (Ex. 23.) 141. In any quadrilateral ABCD inscribed in a circle, the product of the diagonals is equal to the sum of the products of the opposite sides ; that is, AC.DB = AD.BC + AB.DC. (Make the angle DAE=BAC, and prove that AD.BC=AC.DE, and AB.DC -=... | |
 | Edward Olney - 1872 - 562 σελίδες
...joining the centres of the diagonals. 677. In any quadrilateral which may be inscribed in a circle, the product of the diagonals is equal to the sum of the products of the opposite sides. 678. In any triangle the rectangle of two sides is equivalent to the rectangle of the perpendicular... | |
 | George Albert Wentworth - 1884 - 264 σελίδες
...the third side. If AC, BC are taken as the two sides, draw the diameter CE, and join CB. 17. In every inscribed quadrilateral the product of the diagonals...to the sum of the products of the opposite sides. Let ABCD be the quadrilateral. In AC take a point E such that Z EDC= /. ADB. A ADB and CDE are similar;... | |
 | George Albert Wentworth - 1888 - 272 σελίδες
...points where they meet the circumferences, and prove that the A thus formed are similar. 238. In an inscribed quadrilateral, the product of the diagonals...to the sum of the products of the opposite sides. HINT. Draw DE, making Z CDE=ZADB. The A ABD and CDE are similar. Also the A BCD and ADE are similar.... | |
 | George Albert Wentworth - 1889 - 264 σελίδες
...the third side. If AC, BCare taken as the two sides, draw the diameter CE, and join EB. 17. In every inscribed quadrilateral the product of the diagonals...to the sum of the products of the opposite sides. Let ABCD be the quadrilateral. In AC take a point .Esuch that Z EDC= Z ADB. A ADB and CDE are similar;... | |
 | George Albert Wentworth - 1889 - 276 σελίδες
...the third side. If AC, BC are taken as the two sides, draw the diameter CE, and join EB. 17. In every inscribed quadrilateral the product of the diagonals...to the sum of the products of the opposite sides. Let ABCD be the quadrilateral. In AC take a point E such that Z EDC= Z ADB. A ADB and ODE are similar;... | |
 | George Irving Hopkins - 1891 - 208 σελίδες
...proportionally by the circumference of the smaller. 381. In any quadrilateral inscribed in a circle, the product of the diagonals is equal to the sum of the products of the opposite sides. Sug. From one vertex draw a line to the opposite diagonal, making the angle formed by it and one side... | |
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In any inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides. 
