...one of them ; and shew that there may, according to circumstances, be two solutions, one, or none. 7. Describe a circle which shall pass through two given points, and have its centre in a given line. 8. From two given points on the same side of a given line, draw two lines which shall meet in...

...Prop. 7. With a given radius, describe a circle which shall pass through two given points. Prop. 8. Describe a circle which shall pass through two given points, and have its centre in a given line. Prop. 9. In a given circle, inscribe a triangle equiangular to a given triangle. Prop. 10. From...

...points of a triangle. 2. To bisect a triangle by a line drawn from a given point in one of its sides. 3. Describe a circle which shall pass through two given points, and have its centre in a given line. 4. Through a given point to draw a line that shall be equally inclined to two given lines. 5....

...Prop. 7. With a given radius, describe a circle which shall pass through two given points. Prop. 8. Describe a circle which shall pass through two given points, and have its centre in a given line. Prop. 10. From one extremity of a line which can not be produced, draw a line perpendicular to...

...With a given radius, describe a circle which shall pass through two given points. Prop. 8. Describe 9, circle which shall pass through two given points, and have its centre in a given line. Prop. 9. In a given circle, inscribe a triangle equiangular to a given triangle. Prop. 10. From...

...joining their points of intersection is bisected at right angles by the line joining their centres. 72. Describe a circle which shall pass through two given points, and have its centre in a given line. 73. From two given points on the same side of a given line, draw two lines which shall meet in...

...the vertices of a triangle as centre, to describe three circles which shall touch one another. 7. In every right-angled triangle the diameter of the circle...the same side of A B. Let AD, BC intersect in P and AD, BD in Q. Prove that PQ produced is perpendicular to A B. 13. Describe a circle which shall touch...

...a triangle. 2. To bisect a triangle by a st. line drawn from a given point in one of ita sides. 3. Describe a circle which shall pass through two given points, and have iU centre in a giyen line. 4. Through a given point to draw a st. line that shall be equally inclined...

...Prop. 7. With a given radius, describe a circle which shall pass through two given points. Prop. 8. Describe a circle which shall pass through two given points, and have its centre in a given line. Prop. 9. In a given circle, inscribe a triangle equiangular to a given triangle. Prop. 10. From...

...BI= AH, and 2CG = AC = AB = BC; also, OG— CG = OC = OA = OB. * IV. 15. f III. 12. PROBLEM Y. — To describe a circle which shall pass through two given points and have its centre in a straight line given in position. the points A and B, and the line FE in position; that is, ~. the angle...