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Question

If the orthocentre of the triangle formed by the points A(2,0), B(2,3) and C(0,3) is (α,β), then the value of α+β is 


Solution

Given vertices are A(2,0),B(2,3) and C(0,3)
Now, the side lengths are
AB=02+32=3 units
BC=22+0=2 units
AC=22+32=13 units

By observation, we see that
AC2=AB2+BC2
Given triangle is right-angled at vertex B
So, the orthocentre is (α,β)=(2,3)
α+β=2+3=5

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