| Euclid - 1904 - 456 páginas
...an arc of a circle of which the chord is BC. QED PROPOSITION 22. THEOREM. The opposite angles of any **quadrilateral inscribed in a circle are together equal to two right angles.** B Let ABCD be a quadrilateral inscribed in the 0 ABC. Then shall (i) the L." ADC, ABC together = two... | |
| Ontario. Legislative Assembly - 1905
...circumference on the same arc. The angles in the same segment of a circle are equal, with converse. **The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles,** with converse. The angle in a semicircle is a right angle ; in a segment greater than a semicircle... | |
| Queen's University (Kingston, Ont.) - 1906
...circumference on the same arc. The angles in the same segment of a circle are equal, with converse. **The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles,** with converse. The angle in a semicircle is a right angle ; in a segment greater than a semicircle... | |
| Lawrence Robert Dicksee - 1907 - 110 páginas
...sides and the projection of the other side upon it. Q. 8. — Prove that the opposite angles of any **quadrilateral inscribed in a circle are together equal to two right angles.** Show that, if ABC be a triangle and BP, CP be drawn perpendicular to AB and AC respectively to meet... | |
| Henry Sinclair Hall - 1908
...less than the angle BAC by a right angle. THEOREM 40. [Euclid III. 22.] The opposite angles of any **quadrilateral inscribed in a circle are together equal to two right angles.** Let ABCD be a quadrilateral inscribed in the OABC. It is required to prove that (i) the /." ADC, ABC... | |
| Ontario. Legislative Assembly - 1914
...circumference on the same arc. The angles in the same segment of a circle are equal, with converse. **The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles,** with converse. The angle in a semicircle is a right angle; in a segment greater than a semicircle less... | |
| J. L. Heilbron - 2000 - 309 páginas
...ends of the diameters pass through the point of tangency: and probable Junior Optimes had to prove **that the opposite angles of a quadrilateral inscribed in a circle are** supplementary. Figures ii7-ii9 show what is required in these problems. None is difficult. All are... | |
| Victor J. Katz, Annette Imhausen - 2007 - 685 páginas
...matriculation examination at Madras University in 1903 included typical Euclidean problems such as "Prove **that the opposite angles of a quadrilateral inscribed...in a circle are together equal to two right angles"** [Berndt and Reddi 2004, 334]. This Westernized mathematical training naturally influenced the practice... | |
| University of St. Andrews - 1904
...r/p. Prove that the equation whose roots are a4 and ,3* is (p'x + f-)2 - (2pr - <?)*x = 0. & 7. Prove **that the opposite angles of a quadrilateral inscribed...in a circle are together equal to two right angles.** A, B, C, D are i'our points on a circle. If AB and BC be joined and from D perpendiculars DE, DF be... | |
| University of St. Andrews - 1898
...square on this straight line is equal to the sum of the squares on the segments of the hypotenuse. 3. **The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles.** State as many as you know of the properties of a cyclic quadrilateral. ACB is a right-angled triangle... | |
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