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" The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles, with converse. "
Proceedings of the Edinburgh Mathematical Society - Page 11
by Edinburgh Mathematical Society - 1884
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 488 pages
...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...
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Sessional Papers, Volume 37, Part 4

Ontario. Legislative Assembly - Ontario - 1905 - 1096 pages
...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...
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Calendar of Queen's College and University, Kingston, Canada for the Year ...

Queen's University (Kingston, Ont.) - 1906 - 314 pages
...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...
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The Student's Guide to Accountancy

Lawrence Robert Dicksee - Accounting - 1907 - 128 pages
...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...
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A School Geometry, Parts 1-4

Henry Sinclair Hall - 1908 - 286 pages
...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...
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Annual Report, Volumes 2-3

Civil Service Commission of Canada - Civil service - 1910 - 240 pages
...circumference again in D and C; prove that the arc DC is equal to the arc AB. 5. The opposite angles of any quadrilateral inscribed in a circle are together equal to two right angles. What is the converse of this proposition? Is the converse true? 6. If the line joining two points on...
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Calendar, Part 3

University of Calcutta - 1910 - 684 pages
...contained by the whole line and one of th<> parts' may be equal to the square on the other part. 6. Prove that the opposite angles of a quadrilateral inscribed...in a circle are together equal to two right angles. Hence shew that if one of the sides of u quadrilateral inscribed in 3 a circle be produced the exterior...
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Elementary Trigonometry

William Ernst Paterson - Logarithms - 1911 - 262 pages
...twice the angle at the circumference on the same arc. (6) Angles in the same segment are equal, (c) The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. Prop. 23. The tangent at any point is at right angles to the radius drawn to that point. Prop. 24....
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Journal of Education

Education - 1911 - 1334 pages
...less; shew that the greater segment is also divided in medial section. 3. The opposite angles of any quadrilateral inscribed in a circle are together equal to two right angles. 4. A triangle is inscribed in a circle; prove that the sum of the angles in the three segments exterior...
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Regulations and Courses of Study of the Continuation Schools ...

Ontario. Dept. of Education - 1913 - 128 pages
...circumference on the same arc. The angle 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...
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