...of the triangle, the angle opposite to this side, being in a semicircle, is a right angle ; and when the centre falls without the triangle, the angle opposite...than a semicircle, is greater than a right angle. [III. 31. Therefore, conversely, if the given triangle be acuteangled, the centre of the circle falls...

...angle opposite to this side, being in a semicircle, (llI. 31.) is a right angle ; and, if the center falls without the triangle, the angle opposite to...it is, being in a segment less than a semicircle, (nI. 31.) is greater than a right angle : therefore, conversely, if the given triangle be acute-angled,...

...angle ; but the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle. 2. Of two straight lines within a circle, one passes through the centre and cuts, at right angles,...

...right angle ; an angle in a tegment greater than a semicircle is less than a right angle ; and an angle in a segment less than a semicircle is greater than a right angle. (Th. 8) ; that is, one half of 180°, or 90°, which is the measure of a right angle. If the angle...

...greater segment of a circle than a semicircle is less than a right angle, and the angle contained by a segment less than a semicircle is greater than a right angle. In any circle (fig. 41), a perpendicular from the circumference to the diameter is a mean proportional...

...angle ; but the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle. ALGEBRA. I. Specimen Paper, (Time, 8 hours.) 1. Fiud (1) the sum, (2) the difference, of the two expressions—...

...BDC, that is, by a quantity less than half 180° (No. 140), is less than a right angle. 143. The angle in a segment less than a semicircle is greater than a right angle. The segment BAG being less than a semicircle, the segment BDC must be greater than a semicircle, and...

...angle, and the angle in a segment greater than a semicircle is less than a right angle, and the angle in a segment less than a semicircle is greater than a right angle. Let ABDC be a circle and BC its diameter, and therefore BAC a semicircle, then shall the angle BAC...

...angle; and the angle in a segment greater than a semicircle is less than a right angle ; and the angle in, a segment less than a semicircle is greater than a right angle. Let ABC be a ©, of which O is the centre and BC a diameter. Draw AC, dividing the Q into the segments...

...Prop. 21. B. 3), and therefore the angle ABC is also less than a right angle. PART 3.— The angle ABC in a segment less than a semicircle is greater than a right angle. For assume in the opposite circumference any point D, and draw DA and DC. semicircle, is less than...