186 BOOK OF MATHEMATICAL PROBLEMS. 



880. The four conies which can pass through three given 

 points and touch two given straight lines are drawn, and their 

 other common tangents drawn to every two ; prove that the six 

 points of intersection will lie by threes on four straight lines ; and 

 that the diagonals of the quadrilateral formed by these four 

 straight lines pass each through one of the three given points. 



881. Two conies intersect in A , .#, (7, D ; through D is 

 drawn a straight line to meet the curves again in two points ; 

 prove that the locus of the point of intersection of the tangents 

 at these points is a curve of the fourth degree and third class, 

 having cusps at A, B, C, and touching both conies. 



882. Prove that the envelope of the straight line joining the 

 points of contact of parallel tangents to two given parabolas is a 

 curve of the third degree and fourth class ; having three points of 

 inflexion the tangents at which are the common tangents of the 

 parabolas. 



