In an isosceles triangle, the circumcenter, the incentre, the orthocenter and the centroid are-

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Collinear

Coincide

Do not coincide

None of the above

answer is A.

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Detailed Solution

Let suppose a triangle ABC, in which,
Question Image

AB=AC (isosceles triangle)
Now draw perpendicular from A to BC at point D such that,
AD ⊥ BC.
Here, BD = DC also,
∠BAD = ∠DAC
Here, we can see that circumcenter, orthocenter, incenter and centroid of the triangle ABC lie on the same line which is AD.
So, in any isosceles triangle circumcenter, orthocenter, incenter and centroid are collinear.
Correct option is 1.

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