Find the area of circumcircle of triangle ABC?

Statement 1: One of external angles of the triangle is $$90^o$$ and largest side is 10 cm.

Statement 2: The triangle has a perimeter of 24 cm, with its smallest angle measuring $$45^o$$.

We need to find the radius of circumcircle to find its area. Now lets look at the statements.

1) One of external angles of the triangle is $$90^o$$ and largest side is 10 cm.

It is given that one of the external angles is $$90^o$$. This says that the triangle ABC is a right-angled triangle. We are also told that the largest side is 10cms. So, this is the length of hypotenuse.

We know that for right angled triangle, half of hypotenuse is the circumradius. So, the radius is 5cm. Area = 25$$\pi$$

2) The triangle has a perimeter of 24 cm, with its smallest angle measuring $$45^o$$.

We need the lengths of all sides, to find the circumradius. But using only this statement, we only know one angle. So, we can't arrive at circumradius using this data.

So, option A is the correct answer.