The circumcentre of a triangle with the vertices (a,0). (0,b) and (a, b).
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The circumcentre of a triangle with the vertices (a,0). (0,b) and (a, b).
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Step-by-step explanation:
Step 1 :
Given coordinates A(0,0),B(3,0),C(0,4)
Finding the midpoint of AB
=(
2
3+0
,
2
0+0
)
=(
2
3
,0)
Now by finding the slope of AB=(
3−0
0−0
=0)
Now , slope of perpendicular bisector is negative reciprocal of AB that is slope of the bisector =∞.
Step 2 :
Finding the equation of AB with the point (
2
3
,0) is
x=
2
3
is equation of the bisector of AB.
Similarly, if we find the equation of bisector of AC we have
Equation of bisector of AC=>y=2
Step 3 :
Hence the coordinates of the circumcenter of the given triangle is (
2
3
,2).