Some triangles are quite special!

Geometry Level 1

Consider an isosceles △ A B C \triangle ABC with A B = A C = 5 , B C = 6 , AB=AC=5, BC=6, where I , O , H I,O,H denote its incenter, circumcenter, orthocenter, respectively.

Find the area of △ I O H \triangle IOH .


The answer is 0.000.

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Nihar Mahajan by Nihar Mahajan , 20, India

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2 solutions

Piyush Parwani
Aug 8, 2015

In an isosceles triangles all the three centres (incenter, orthocenter and circumcenter) fall in a straight line. Therefore no triangle is formed and hence the area is zero. □ \square

5 Helpful 1 Interesting 0 Brilliant 1 Confused

what about the centroid?

Jia Varshney - 1 year, 7 months ago

Since A B = A C AB=AC , we have I , O , H I, O, H are collinear.

So the area of Δ I O H = 0 \Delta IOH=\boxed{0} .

4 Helpful 1 Interesting 1 Brilliant 0 Confused

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