...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...

...is this impossible ? (24) Answer either 6 a or 6 b, not both. 6 a. Prove that opposite angles of any quadrilateral inscribed in a circle are together equal to two right angles. (12) 6 b. Prove that the angle in a semicircle is a right angle, and that the angle in a segment of...

...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...

...which is subtended by the same arc, at the circumference of the circle. The opposite angles of any quadrilateral inscribed in a circle, are together equal to two right angles. 23. VARIATION (Continued) LET us now consider the third example of variation given in Chapter 16. In...

...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...

...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...

...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...

...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...

...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...

...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...