Three circles centre A,B and C with radii 4cm, 3cm, 2cm, respectively, touch one another externally.Calculate the lengths of the sides of triangle ABC
draw the figure. Each side is the sum of the two touching radii.
Yes
Three circles centre A,B and C with radii 4cm, 3cm, 2cm, respectively, touch one another externally.Calculate the lengths of the sides of triangle ABC
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To calculate the lengths of the sides of triangle ABC, we can use the formula for the distance between two points, which is the square root of the sum of the squares of the differences in their coordinates. In this case, we can use the centers of the circles A, B, and C as the points.
Let's denote the distance between the centers of circles A and B as d1, between B and C as d2, and between C and A as d3.
Using the formula for the distance between two points, we have:
d1 = sqrt((4 - 3)^2 + (0 - 0)^2)
= sqrt(1^2 + 0)
= sqrt(1)
= 1
d2 = sqrt((2 - 3)^2 + (0 - 0)^2)
= sqrt((-1)^2 + 0)
= sqrt(1)
= 1
d3 = sqrt((4 - 2)^2 + (0 - 0)^2)
= sqrt(2^2 + 0)
= sqrt(4)
= 2
Therefore, the lengths of the sides of triangle ABC are:
AB = d1 + radius of circle A + radius of circle B = 1 + 4 + 3 = 8 cm
BC = d2 + radius of circle B + radius of circle C = 1 + 3 + 2 = 6 cm
AC = d3 + radius of circle C + radius of circle A = 2 + 2 + 4 = 8 cm
So, the lengths of the sides of triangle ABC are 8 cm, 6 cm, and 8 cm.