Question

Three vertices of a triangle are `A(4,3); B(1,-1) and C(7,k)`. Value(s) of `k` for which centroid, orthocentre,incentre and circumcentre of the `DeltaABC` lie on the same straight line is/are-

Answer 1

`/_ABC` is an isosceles triangle
so, AB=AC
squaring both sides
`(AB)^2=(AC)^2`
from point A,B,C we get
`3^2+4^2=3^2+(3-k)^2`
`9+16=9+(3-k)^2`
`(k-3)^2=16`
`(k-3)=+-4`
so, k will be
k=7,-1