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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 - Página 9
por Edinburgh Mathematical Society - 1894
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a gemoetry for schools

...the angle at the circumference (on the same arc). 4. The angle in a semicircle is a right angle. 5. The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. 6. If the opposite angles of a quadrilateral make up two right angles, a circle can be described about...
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A Course of Pure Geometry

...to the radius through the point of contact. 7. Angles in the same segment of a circle are equal. 8. The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. 9. The angle between the tangent at any point of a circle and a chord through that point is equal to...
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Geometry for Young Beginners

...a segment. 2. The angles in a segment are equal. 3. The angle in a semicircle is a right angle. 4. The opposite angles of a quadrilateral inscribed in...a circle are together equal to two right angles*. * This can be seen from the figure 60, and is proved more fully in Section 13. 5. If the opposite angles...
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Annual Calendar of McGill College and University, Montreal

McGill University - 1868
...half the base, and twice the square of the bisecting line. 4. Find the centre of a given circle. 5. The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. 6. Divide a right line similarly to a given divided line, a. Divide a right line into n equal parts....
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A Course of Pure Geometry

...triangle on the opposite sides are concurrent. 7. Angles in the same segment of a circle are equal. 8. The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. 9. The angle between the tangent at any point of a circle and a chord through that point is equal to...
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Calendar

University of St. Andrews - 1891
...of a parallelogram is equal to the sum of the squares on the sides. 12. The opposite angles of every quadrilateral inscribed in a circle are together equal to two right angles. ABC is a triangle : AD, BE are perpendicular to BC, AC respectively : prove that the triangle ODE is...
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The calendar of the University college of Wales

Wales univ, univ. coll. of Wales - 1878
...that parallelograms on the same base and between the same parallels are equal to one another. 8. Prove that the opposite angles of a quadrilateral inscribed in a circle are supplementary. 9. If 0 be a point within a triangle ABC, such that the angles BOG, COA, AOB are equal,...
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Calendar

University of St. Andrews - 1901
...the centre of a circle is double an angle at the circumference standing on the same arc, and deduce that the opposite angles of a quadrilateral inscribed in a circle are supplementary. Two circles ABC, ABD, with centres 0 and Q, intersect at right angles ; AC and AD are...
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A Shorter Geometry

...its angular points, and measure the length of its radius. 7. Prove that the opposite angles of any quadrilateral inscribed in a circle are together equal to two right angles. ABCD is a parallelogram and the circle described about the triangle ABC cuts CD, or CD produced, in...
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Report of the examination held (Dec. 1859)-73

Cowley Oxon, dioc. school - 1860
...which does not pass through the centre it shall cut it at right angles. 10. The opposite angles of any quadrilateral inscribed in a circle are together equal to two right angles. II. Describe an isosceles triangle having each angle at the base double the third angle. 12. If two...
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