AK i GEOMETRY [<'n. VII 



32. An equilateral triangle is inscrilw.l in th- circle x 4 + y* = 4 \viili 

 its base parallel to the Z-UXIH; through its vertices tangents to the circle 

 are drawn, thus forming a circumscribed triangle; find the equal 

 and the lengths, of the sides of each triangle. 



33. The poles of the sides of each triangle in example 82 are the 

 vertices of a triangle; find the equations of its sides, and draw tin t; 



34. A chord of the circle x* + y f - 22*- 4y + 25 = is of length 

 4 Vo, and is parallel to the line 2 x + y + 7 = 0; find the equation of the 

 chord, and of the normals at its extremities. 



35. Fiml the equation of a circle through the intersection of the 

 circles x*+ y* - 4 = 0, x* + y* - 2x - 4y + 6 = 0, and tangent to tin- I'm.- 

 x + y - 3 = 0. 



36. The length of a tangent, from a moving point, to the cin ! 

 a:*+y*=6 is always twice the length of the tangent from the same point 

 to the circle ar* + y 2 + 3 (x + y) = 0. Find the equation of the locus of 

 the moving point. 



37. Find the locus of the vertex of a triangle having given the base 

 = 2 a, and the sum of the squares of its sides = 2 1 1 . 



38. Fiml the locus of the middle points of chords drawn through a 

 fixed point on the circle x a + y 2 = a 8 . 



39. Through the external point P l = (x v y t ) t a line is drawn meeting 

 the circle z 2 + y 2 = a 2 in Q and R; find the locus of middle point oi 



as this line revolves about P r 



40. A point moves so that its distance from the point (1, 3) is to its 

 distance from the point (~4, 1) in the ratio 2:3. Find the equ 



of its locus. 



41. Do the circles 



4x + 4y + 4*-12y + l=0 and 2*' + 2y + y = 

 intersect? Show in two ways. 



42. Find the equation of a circle of radius V85 which passes through 

 the points (2, 1) and (-.3, 4). 



43. What an* the equations of the tangent and the normal to the 

 circle x* + y 2 = 1 3, these lines passing through the point (2, -:'*)? 

 through the point (0, 6) V 



44. Find the equations of the tangents through (2, 3) to the circle 





