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" The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles. "
Pure Mathematics - Page 273
1874
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Recent military, naval, and civil service examination papers in mathematics ...

1874
...the centre, it shall cut it at right angles ; and if it cut it at right angles it shall bisect it. 6. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. From the point A in the circumference of the circle APQB three chords AP, AQ, and AB are drawn so that...
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University Calendar

Madras - 1874
...line AB in C so that the rectangle contained by AC, CB may be twice the square on AC. II. Provp that the opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. Also state and prove the converse of this proposition. III. Inscribe a circle in a given triangle....
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

James Bryce - 1874
...III. 22).— Hence also if a quadrilateral figure be inscribed in a circle, its two opposite angles are together equal to two right angles. Let ABCD be a quadrilateral figure inscribed in a circle, any two of its opposite angles are together equal to two right angles. Join the centre 0...
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Examination Christmas,1875

Education Department,London - 1876
...В are tangents at A, B, and AD is a diameter. Shew that the angle AC В is twice the angle BAD. 3. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. The lines bisecting any angle of the inscribed quadrilateral and the opposite exterior angle meet in...
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Elements of geometry, based on Euclid, Books 1-3

Edward Atkins - 1876
...<fee. QED mid also = 2 i BED. .'. ^ BAD = i. BED. i BAC = /: EEC, and i CAD = ^ CED. .-. i BAD = ^ UED. Proposition 22.— Theorem. The opposite angles of...any quadrilateral figure inscribed in a circle are togetlier equal to two right angles. Let ABCD be a quadrilateral figure inscribed in the circle ABCD....
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Unterricht, Erziehung und Fortbildung. 2 Bde. [in 3pt ..., Volume 2, Part 2

H. Loehnis - 1876
...bo equal to a given rectilineal figure. ADDITIONAI, GEOMETRY. 7. Prove that the opposite angles of a quadrilateral figure inscribed in a circle are together equal to two right angles. When can a parallelogram be inscribed in a circle ? 8. Rectangles of the same altitude are one to another...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 403 pages
...to the whole angle BED. (ax. 2.) Wherefore the angles in the same segment, &c. QED PROPOSITION XXII. THEOREM. The opposite angles of any quadrilateral figure inscribed in a circle, art together equal to twu right angles. Let ABCD be a quadrilateral figure in the circle ABCD. Then...
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Solutions to the mathematical examination papers set for admission to the ...

D. Tierney - 1877
...straight line which joins their centres being produced, shall pass through that point of contact. 7. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. From the point C, the straight lines CA and CB are drawn touching the circle PAB whose centre is O...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878
...eirck from a point, cither within its circumference or without it. PROP. XLI. TIIEOREM. (E. 3. 22). The opposite angles of any quadrilateral figure inscribed...in a circle, are together equal to two right angles and conversely if the opposite angles of a quadrilateral figure are together equal to two right angles,...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1878 - 349 pages
...equiangular to each other. PROPOSITION XXII. THEOREM. The opposite angles of any quadrilateral figure, i a circle, are together equal to two right angles. Let ABCD be a quadrilateral fig. inscribed in a 0 . Then must each pair of its opposite L s be together equal to two rt. L s. Draw...
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