show that the points (3,4),(0,5),(-3,-4),(-5,0) are concyclic and find the radius of the circle?

Question

circle question

Answer 1

(x-h)^2+(y-k)^2=r^2 where (h,k) is the circle's centre and r is the radius.

Substitute the points:

h^2+(5-k)^2=r^2=(5+h)^2+k^2

h^2+25-10k+k^2=25+10h+h^2+k^2

-10k=10h, k=-h

(3-h)^2+(4-k)^2=(3+h)^2+(4+k)^2

9-6h+h^2+16-8k+k^2=9+6h+h^2+16+8k+k^2

-12h-16k=0, 3h+4k=0, and k=-h so h and k are zero, therefore r=5 (x^2+y^2=25).