i) We know that,
In any triangle, line drawn parallel to one side, passing through mid-point of another side will also meet the third side at its mid-point.
Let AD be ‘x’, then DC = x. similarly AE = y then EB = y
By pythagorus theorem for bigger triangle ABC,
Similarly for smaller triangle AED,
From 1 & 2, we have
We have the above following data.
And from pythagorous theorem,
Hence the distance between mid-point of hypotenuse to vertex B (or) A (or) C is x
iii) We know that
circumcentre is a point from which all the vertices are at equal distances.
In the above case, we have proved the mid-point of hypotenuse is equidistant from all the three vertices. Therefore mid-point of hypotenuse is the circumcentre of the given triangle.
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