Calendar: 1873-1874 Page 607

THE SCHOOL 607 Also describe circle of given radius touching given straight line and given circle In each case find how many circles can be drawn Describe on given straight line segment of circle containing an angle equal to given rectilineal angle 10 Describe an isosceles triangle having each of the angles the base double of the third angle 11 are the centres of two circles which touch inter- nally at and also touch third circle whose centre is externally and internally respectively at prove that the angle ABB is double of the angle ECF 12 If the vertical angle of triangle be bisected by straight line which also cuts the base the segments of the base shall have the same ratio which the other sides of the triangle have to one another Having given the base and the ratio of the sides of triangle find the locus of its vertex 13 Similar triangles are to one another in the duplicate ratio of their homologous sides 14 If two straight lines be at right angles to the same piano they shall be parallel to one another 15 Define sphere and tetrahedron Show bow to inscribe sphere in and to describe sphere about given tetrahedron £ac i0 II Draw from given point straight line equal to given straight line Draw straight line perpendicular to given straight line of unlimited length from given point without it Find point in given straight line which is equidistant from two given points Any two sides of triangle are together greater than the third side