Circle area formula: Radius of circle inscribed in a triangle

Radius of circle inscribed in a triangle = A s Where, A = Area of triangle, s =Semi-perimeter of triangle = a + b + c 2 Note a,b,c are sides of the triangle So, s = 3 +9 +7 2 = 19 2 = 9.5 We can find the area of triangle using Heron's formula : Heron's formula : Area = √s(s − a)(s − b)(s −c) → Area = √9.5(9.5 −3)(9.5 −9)(9.5 − 7) Area = √9.5(6.5)(0.5)(2.5) Area = √9.5(8.12) Area = √77.14 = 8.78 Radius = A s = 8.78 9.5 = 0.92... 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 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 ... The area of the circle is 9picm^2 or 28.26cm^2. From the perimeter (circumference) of a circle , we can calculate the radius, which we can then use to calculate the area of the circle . The formula for circumference of a circle is: C=2pir, where C=Circumference, and r=radius. Using the given data: 6pi=2pir Cancel the like terms on both sides. 6cancelpi=2cancelpir Divide both sides by 2. 3=r Now that we know the radius is 3cm, we calculate the area with the formula : A=pir^2 A=pixx3^2 A=pixx9 A ...