Concyclic points⭕
A circle is constructed using three concyclic points (8,6) , (7,7) , (4,8) .
The circle cuts the Y-axis at (0,y) and cuts the X-axis at (x,0) and also cuts origin.
Find the value of x+y .
This is an original problem and belongs to my set Raju bhai's creations
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1 solution
Since the circle passes through the origin it is of the form: x 2 + y 2 + 2 g x + 2 f y = 0
The circle passes through the points ( 8 , 6 ) , ( 7 , 7 ) , ( 4 , 8 ) . Substituting for x and y in the above equation and solving for g and f gives us
g = − 4 f = − 3
Therefore, the equation of the required circle is x 2 + y 2 − 8 x − 6 y = 0 .
For x = 0 : y = 0 or y = 6
For y = 0 : x = 0 or x = 8
Therefore, the point of intersection with Y axis is ( 0 , 6 ) and that with X axis is ( 0 , 8 )
Hence, the value of x + y = 8 + 6 = 1 4