 | Alan Sanders - 1903 - 392 σελίδες
...from A to any point on CD. Prove that AE x AF is A constant. [A circle can be passed through F, B, G, and E. (?)] 46. Given the vertical angle, the medial...fourth of BC. AE cuts the diagonal BD in F. Show that SF is one fifth of BD. 64. Two chords of a circle drawn from a common point A on the circumference... | |
 | Alan Sanders - 1903 - 396 σελίδες
...ABCD, BF is drawn cutting the diagonal AC in E, CD in G, and AD prolonged in JF*. Prove that BE3 = ClE x EF. 49. If three circles intersect each other, their...diagonal BD in F. Show that BF is one fifth of BD. 54. Two chords of a circle drawn from a common point A on the circumference and cut by a line parallel... | |
 | Fletcher Durell - 1911 - 553 σελίδες
...Rf} respectively. Prove the triangles PQR and P'Q'R1 similar. BOOK III. PLANE GEOMETRY Ex. 10. In an inscribed quadrilateral, the product of the diagonals...to the sum of the products of the opposite sides. [SUG. Draw BF so that ^.CBF=£ABD and use similar triangles.] Ex. 11. The sum of the squares of the... | |
 | Fletcher Durell - 1904 - 382 σελίδες
...B,', respectively. Prove the triangles PQR and P'Q'B' similar. BOOK ~III. PLANE GEOMETRY Ex. 10. In an inscribed quadrilateral, the product of the diagonals...the sum of />• the products of the opposite sides. [Sua. Draw BF so that Z CBF= Z ABD and use similar triangles.] . Ex. 11. The sum of the squares of... | |
 | George Albert Wentworth - 1904 - 496 σελίδες
...points where they meet the circumferences. The & thus formed are similar (Ex. 120). Ex. 263. In an inscribed quadrilateral, the product of the diagonals...to the sum of the products of the opposite sides. Draw DE, making Z CDE = Z ADB. The & ABD and ECD are similar ; and the & BCD and AED are similar. Ex.... | |
 | Fletcher Durell - 1904 - 382 σελίδες
..., respectively. Prove the triangles PQB and P'QfB' similar. BOOK III. PLANE GEOMETRY Ex. 10. In an inscribed quadrilateral, the product of the diagonals is equal to the sum of B the products of the opposite sides. [Sue. Draw BF so that Z CBF= Z ABD and use similar triangles.]... | |
 | Levi Leonard Conant - 1905 - 140 σελίδες
...angle DCA is equal to the angle EAB. If AB = 25 in., AD = 13 in., and BU= 1 in., find CA and CB. 520. In any inscribed quadrilateral the product of the...to the sum of the products of the opposite sides. HINT. Let A BCD be the quadrilateral. In the diagonal AC take a point E such that the angle EDC shall... | |
 | Arthur Latham Baker - 1905 - 82 σελίδες
...avoid getting the proper equations, either for the A, or for the elimination of A and B. 33. In an inscribed quadrilateral the product of the diagonals...to the sum of the products of the opposite sides. In accordance with the suggestion of § 31 we mark one line y as unknown, and the conclusion is y (p... | |
 | 1906 - 828 σελίδες
...other, their common tangent is a mean proportional between their diamtters. 5. Demonstrate : In an inscribed quadrilateral, the product of the diagonals...to the sum of the products of the opposite sides. 6. Demonstrate : The area of an inscribed regular octagon is equal to that of a rectangle whose sides... | |
 | Isaac Newton Failor - 1906 - 431 σελίδες
...between the perpendiculars from P to the tangents drawn from the extremities of the chord. 764 In an inscribed quadrilateral, the product of the diagonals...to the sum of the products of the opposite sides. PROPOSITION XXXV. PROBLEM 384 To divide a given straight line into segments proportional to any number... | |
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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. 
