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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 ... Area of circumscribed circle is 194.5068 If the sides of a triangle are a, b and c, then the area of the triangle Delta is given by the formula Delta=sqrt(s(s-a)(s-b)(s-c)), where s=1/2(a+b+c) and radius of circumscribed circle is (abc)/(4Delta) Hence let us find the sides of triangle formed by (4,6), (2,9) and (8,4). This will be surely distance between pair of points, which is a=sqrt((2-4)^2+(9-6)^2)=sqrt(4+9)=sqrt13=3.6056 b=sqrt((8-2)^2+(4-9)^2)=sqrt(36+25)=sqrt61=7.8102 and c=sqrt((8-4 ... 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. The area of a circle of radius r is given by the well known formula : A = πr2 If the diameter is d the we have d = 2r ⇒ r = d 2, thus we have: A = π(d 2)2 = πd2 4 Thus, we have: d = 4 ⇒ A = π42 4 = 4π d = 9 ⇒ A = π92 4 = 81 4 π d = 11 ⇒ A = π112 4 = 121 4 π
