Draw a right triangle and the perpendicular from the midpoint of the hypotenuse to the base.
i) Prove that this perpendicular is half the perpendicular side of the large triangle.
ii) Prove that this perpendieular bisects the bottom side of the larger triangle.
iiii) Prove that in the large triangle, the distances from the midpoint of the hypoteniuse to all the vertices are equal.
iv) Prove thàt the circumcentre of a right triangle is the midpoint of its hypotenuse.