Mathematics

In figure A and B are the centres of the two intersecting circles.
With the help of Euclid's first axiom, state the type of $$\Delta ABC$$.


ANSWER

An equilateral triangle.


SOLUTION
From the above figure, AB and AC are the radii of the circle on the left, where C is the point of intersection of the two circles.

Similarly, BA and BC are the radii of the circle on the right, where C is the point of intersection of the two circles.

We know, AB = AC and BC = AB, then by Euclid's first axiom, AC = BC.
Hence AC = BC = AB which makes triangle ABC an equilateral triangle.
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