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Question

If the points (2,0),(0,1),(4,5) and (0,c) are concyclic, then the value of c is

A
1
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B
1
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C
143
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D
143
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Solution

The correct options are
B 1
C 143
Solution -
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
(x2)2+y2=x2+(y1)2...(1)
(x2)2+y2=(x4)2+(y5)2...(2)
From (1)
4ax=12y...(3)
From (2)
4x=3710y...(4)
Afters solving
x=136,y=176
equating the distance of different point from center
(1362)2+(176)2=(1360)2+(176c)2
136+28936=16936+(176c2)36
121=(176c)2
176c=±11
C=1,143
Option B,C are correct

1048974_460049_ans_aa8325a2c6c049e48021ccbe08888af2.png

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