Drawn an isosceles triangle. Locate its centroide, orthocentre, circumcentre and incentre. Verify that they are collinear.

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Solution

In $△ A B C, A B = A C, A D ⊥ B C ⟹ B D = B C ⟹ ∠ B A D = ∠ D A C$
$∵ A D ⊥ B C,$ orthocentre lies on $A D$
$B D = B C,$ centroid lies on $A D$
$∠ B A D = ∠ D A C,$ incentre lies on $A D$
$∴$ centroid,orthocentre,circumcentre,incentre are collinear

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