finding the length of tangents?

Question

1)the lengths of the tangents from the potint (4,k) to the circle x^2 + y^2 = 9 are 4sqroot2. find the possible values of the constant k.

i think the answer is + or - 5 but am unsure on the working

2) show that the tangents from the point (3,-4) to the circles x^2 + y^2 + 2x - 4y + 4 = 0 and x^2 + y^2 +4x - 4y -2 =0 are equal in length

Answer 1

The distance of(4,k) to the center is d^2 = 16+k^2
16+k^2= 9 +32 so k^2= 25 and k=+-5
2) C1(-1,2) radius^2= 1 (distance to center)^2= 52
length ^2 = 52-1 =51
C2 (-2,2) radius ^2 =10 distance to center ^2= 61
length ^2= 61-10=51
(proved)
Remember :The given point the center and the contact point form a right angle triangle)

Answer 2

don't you just take the square root of 9 and devide by two?? I don't have trig calculater. just the financial calculator at home. i'm not exactly sure i understand the question. Duh. its a circle. the distance from the center to the perimeter is PI devided by 6 right. such as one inch round devided by .866 equals the distance across corners of a hexigon. ( I figured that out at work by accident a couple years ago. the distance from the center is the same length as the distance from point to point on a hex. so draw me a picture i'll figure it out. or i'll take to work and let the guys help. there is no trig. the can't figure out.