Question

Find the circumcenter of the triangle whose sides are x= 1, y=1 and x+y=1​

Answer 1

SOLUTION

TO DETERMINE

The circumcenter of the triangle whose sides are x= 1, y=1 and x+y=1

EVALUATION

Here the given lines are

x= 1

y=1

x + y = 1

The given lines form a Right angled triangle BCD with Right angle at B

So the hypotenuse = CD

Now we know in case of Right angle triangle Circumcenter is the midpoint of the Hypotenuse and the Hypotenuse is the Diameter of the Circle

So the coordinates of C and D are ( 1,0) & (0,1) respectively

Hence the midpoint (A) of the Hypotenuse ( CD) is

$\displaystyle \sf{ = \bigg( \frac{1 + 0}{2} \: , \: \frac{0 + 1}{2} \bigg) \: }$

$\displaystyle \sf{ = \bigg( \frac{1}{2} \: , \: \frac{ 1}{2} \bigg) \: }$

Hence the circumcenter of the triangle whose sides are x= 1, y=1 and x+y=1 is

$\displaystyle \sf{ = \bigg( \frac{1}{2} \: , \: \frac{ 1}{2} \bigg) \: }$

GRAPH

The figure is referred to the attachment

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