let each of circles
S1≡x2+y2+4y-1=0
S2≡x2+y2+6x+y+8=0
S3≡x2+y2-4x-4y-37=0
touches the other two. let P1,P2,P3 be the point of contact of S1 and S2, S2 and S3, S3 and S1 respectively. let T be the point of concurrence of the tangents at P1, P2, P3 to the circles C1, C2, C3 are the centres of S1, S2, S3 respectively.
1) P2 and P3 are the reflections of each other in the line.......
2) the area of the quadrilateral TP2C3P3 is............
3) the ratio of the area of ΔP1P2P3 to ΔC1C2C3 is......
39Radii of the circles are :
R1 : √5
R2 : √5/2
R3 : 3√5
Common tangent of S1 and S2 is
T1 : 6x - 3y + 9 = 0 => y = 2x + 3
Similarly,
T2 : 2x + 2y + 9 = 0 => y = -x - 9/2
T3 : x + 2y + 9 = 0 => y = -x/2 - 9/2
Point of contact is (-a2m/c, a2/c).
P1 : (-2 x 5/3, 5/3) or ( -10/3, 5/3 )
P2 : (5/18, -5/18)
P3 : (5, 10)
Some silly mistake I've made...P2 and P3 don't seem reflections at at all.
