Question

if two circles are congruent then their ______ are equal.

Answer 1

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Answer 2

If two circles are congruent then their radius is equal.

Let x be the two congruent circles

and y be the equal radius of the circles.

Now, we assume that the circles are congruent which also means that the area of both the circle is also equal.

Let the radius of two circles be $r_{1}$ and $r_{2}$.

    The area of circles are equal so,

         ⇒ $\pi r^{2} _{1} = \pi r^{2} _{2}$

         ⇒ $r^{2} _{1} = r^{2} _{2}$

         ⇒ $r_{1} = r_{2}$

So, the radius of the two circles is equal which means the circles are of the same size.

then both the circles are congruent.

Hence, proved.