If the sum of circumferences of two circles wirh radii r1 & r2 is equal to the circumference of a circle of radius r, then what is true
1 r1+ r2 = r or sum of their squares= r2
"sum of circumferences of two circles wirh radii r1 & r2"
= 2πr1 + 2πr2
"the circumference of a circle of radius r"
= 2πr
they are equal ....
2πr1 + 2πr2 = 2πr
2π(r1 + r2) = 2πr
divide both sides by 2π
To solve this problem, we need to use the formula for the circumference of a circle, which is given by:
C = 2πr
Let's first consider the first statement: r1 + r2 = r.
If the sum of the radii of two circles, r1 and r2, is equal to the radius of a third circle, r, we can substitute these values into the formula for the circumference:
C1 + C2 = 2πr1 + 2πr2 = 2π(r1 + r2)
Now, let's consider the second statement: the sum of their squares = r^2.
If we square both r1 and r2, and then sum them, we have:
r1^2 + r2^2
In order to determine which statement is true, we can examine the equation for the circumference of a circle given the sum of two circumferences:
2π(r1 + r2) = 2πr
Dividing both sides of the equation by 2π, we have:
r1 + r2 = r
Therefore, the first statement, r1 + r2 = r, is true when the sum of circumferences of two circles with radii r1 and r2 is equal to the circumference of a circle of radius r.