Circle area formula: If a

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 ... The surface area of a general ellipsoid cannot be expressed exactly by an elementary function. However an approximate formula can be used and is shown below: 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 ... 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 ...