...this square determines the required point on AB. The proof from m. 11 and III. 12. 8. To construct an isosceles triangle having each of the angles at...third angle. Take any straight line AB, and divide it so that AB.BC = With centre A and distance AB describe a circle, in which place BD = AC. Join AD; ABD...

...what parallelograms can circles be inscribed ? 15. Give the analysis and synthesis of the problem : to describe an isosceles triangle, having each of the angles at the base double of the third angle ? 16. Shew that in the figure Euc. iv. 10, there are two triangles possessing the required property...

...have also a circle described about it the area of thii circle is double that of the first circle. S. Describe an isosceles triangle having each of the angles at the base double of the third angle.—Apply this proposition directly to inscribe au equilateral and equiangular decagon in a given...

...constructed on DF as the one given line is to the other. PROBLEM XXXIV. 339. Upon a given base to construct an isosceles triangle, having each of the angles at the base double the vertical angle. Let AB be the given base. Produce AB to some point C till the rectangle ACXBC shall...

...constructed on DF as the one given line is to the other. PROBLEM XXXIV. 339. Upon a given base to construct an isosceles triangle, having each of the angles^ at the base double the vertical angle. Let AB be the given base. Produce AB to some point C till the rectangle AC X BC...

...describe a circle : the circle ABCD is about the given square. (9. IV.) PROB. 10. To describe an isoecelee triangle Having each of the angles at the base double of the third angle. x"' E — Take any line AB, and, by 11. II., divide it so that the -• rectangle AB . BC shall equal...

...made by this line with the tangent are equal to the angles in the alternate segments of the circle. 4. To describe an isosceles triangle having each of the angles at the base double the third angle. 5. In right angled triangles, the rectilineal figure described upon the side opposite...

...B, C, D, and will be described about the square, as was required. Q. is. F. PROPOSITION X. PROBLEM. To describe an isosceles triangle, having each of...angles at the base double of the third angle. Take any st. line AB and divide it in C, BO that rect. AB, BC = sq. on AC. II. 11. With centre A and radius...

...centre is greater than the one more remote. 3. If through the angles of an isosceles triangle which has each of the angles at the base double of the third angle, and is inscribed in a circle, straight lines be drawn touching the circle ; show that an isosceles...

...any two opposite sides of the square subtends a right angle at the centre of the circle. 7. Construct an isosceles triangle, having each of the angles at the base double of the third angle. If ABC be such a triangle, where A is the less angle, and if from A AD be drawn, so that the angle...