 | Great Britain. Education Department. Department of Science and Art - 1886 - 640 pages
...What property of the circle follows from this theorem ? (20.) 29. Show that the opposite angles of any quadrilateral inscribed in a circle are together equal to two right angles. Two given circles intersect in A and B ; on the circumference of one of them take any two points C... | |
 | 1887 - 644 pages
...chord CD at right angles in E. Prove that the centre of the circle is F the middle point of AB. 8. The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. 9. From a point A on a circle ADE draw a chord AD cutting off a segment ADE containing an angle equal... | |
 | University College, Dundee - 1889 - 358 pages
...produced approaches indefinitely near to the tangent at P as Q approaches indefinitely near to P. 6. The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. ABCD is a quadrilateral inscribed in a circle ; BA, CD meet in P ; CB and DA in Q. Prove that if a... | |
 | Education - 1890 - 714 pages
...of 16 x* — i, x — 4x' and i — 8 x •+• i6x>. PLANE GEOMETRY. 1. Two opposite angles of any quadrilateral inscribed in a circle are together equal to two right angles. 2. About a given circle, describe a triangle similar to a given triangle. 3. If the vertical angle... | |
 | 1891 - 718 pages
...the ratio 5 ; 7. PUEE MATHEMATICS.— PART I. The Board of Examiners. 1. The opposite angles of any quadrilateral inscribed in a circle are together equal to two right angles. Show that a circle can always be drawn through the angular points of a quadrilateral having two opposite... | |
 | Joseph Edwards - Mathematics - 1892 - 550 pages
...p-qx and q-px tend to equality as x diminishes to zero, but yet that their limits are not equal. 11. The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. What does this become when in the limit two angular points coincide ? 12. Find the ultimate position... | |
 | Euclid - Geometry - 1892 - 460 pages
...with equal vertical angles is an arc of a circle. PROPOSITION 22. THEOREM. 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 ijABC; then shall, (i) the L. s ADC, ABC together = two... | |
 | 1896 - 154 pages
...given straight line, which is less than half the straight line divided. 2. The opposite angles of any quadrilateral inscribed in a circle are together equal to two right angles. In what propositions does Euclid make use of this result ? If from any point c in the circumference of... | |
 | Joe Garner Estill - 1896 - 186 pages
...polygon. Prove that every equiangular polygon circumscribed about a circle is a regular polygon. 5. Prove that the opposite angles of a quadrilateral inscribed in a circle are supplements of each other. 6. Construct a square, having given its diagonal. 7. Prove that the area... | |
 | Joe Garner Estill - 1896 - 214 pages
...polygon. Prove that every equiangular polygon circumscribed about a circle is a regular polygon. 5. Prove that the opposite angles of a quadrilateral inscribed in a circle are supplements of each other. 6. Construct a square, having given its diagonal. 7. Prove that the area... | |
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The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles, with converse. 
