The distance between orthocentre and circumcentre of the triangle with vertices (2,3) (2,5) (4,3)
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Answer:
Let A(2,1,5), B(3,2,3), and C(4,0,4) be the vertices of the triangle given.
We have the distance formula, between points P(x
1
,y
1
,z
1
) , R(x
2
,y
2
,z
2
)
PR=
(x
1
−x
2
)
2
+(y
1
−y
2
)
2
+(z
1
−z
2
)
2
To find the length of the sides,
AB=
(2−3)
2
+(1−2)
2
+(5−3)
2
=
1+1+4
=
6
CB=
(4−3)
2
+(0−2)
2
+(4−3)
2
=
1+4+1
=
6
CA=
(4−2)
2
+(0−1)
2
+(4−5)
2
=
4+1+1
=
6
⟹The triangle is equilateral.
Hence the ortho-centre, circumcentre, incentre and centroid is the same point.
The distance between ortho-centre and circumcentre is 0.
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