Question

find the value of C so that(2,0), (0,1), (4,5),(0,c) are concyclic.​

Answer 1

Answer:

Let (x,y) be the center of the circle 

All points (2,0),(0,1),(4,5),(0,C) are equidistant 

from the circle 

Let us find out x,y by making two equations 

(x−2)2+y2=x2+(y−1)2...(1)

(x−2)2+y2=(x−4)2+(y−5)2...(2)

From (1)

4−ax=1−2y...(3)

From (2)

4x=37−10y...(4)

Afters solving 

x=613,y=617

equating the distance of different point from center 

(613−2)2+(617)2=(613−0)2+(617−c)2

361+36289=