Circle area formula: Yes

Yes, larger circle would envelop the smaller circle . Area of the circle centered at (5,4) is 15 pi, hence its radius would be r_1 = sqrt 15 = 3.87 [using circle area formula pi r^2] Likewise the area of the circle centered at (2,1) is 75pi, hence its radius would be 5sqrt3=8.66 The distance between the two centres would be sqrt((5-2)^2 +(4-1)^2)= sqrt 18= 3sqrt2#= 4.24. Since radius of the circle centered at (2,1) is 8.66 which is greater than the distance between the two centres Plus the ... color(blue)("Circles intersect") First we find the radii of A and B. Area of a circle is pir^2 Circle A: pir^2=81pi=>r^2=81=>r=9 Circle B: pir^2=36pi=>r^2=36=>r=6 Now we know the radii of each we can test whether they intersect, touch in one place or do not touch. If the sum of the radii is equal to the distance between the centres, then the circles touch in one place only. If the sum of the radii is less than the distance between centres, then the circles do not touch If the sum of the ... Explanation: In order to find the area of the circumscribed circle , we need to find its radius. There is a formula to do this, although it is a little troublesome. The formula for the circumradius is: R= abc/4A where R is the circumradius, a,b,c are the sides of the triangle, and A is the area of the triangle. If a,b and c are the lengths of the sides and S is the area of the triangle the radius of the inscribed circle is given by the formula : r=(2S)/(a+b+c) The area S can ...