Question

If c1= 80 what is the value of c3

Answer 1

firstly let's find the radius of C1

`\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=80 \end{cases}\implies 80=2\pi r\implies \cfrac{80}{2\pi }=r\implies \cfrac{40}{\pi }=r`

now, that's the radius for C1, looking at the line L, we can see that C2 has half that radius and C3 has half C2's or namely C3 has 1/4 of the radius of C1.

`\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=(1)/(4)\cdot (40)/(\pi ) \end{cases}\implies C=2\pi \cdot \cfrac{1}{4}\cdot \cfrac{40}{\pi }\implies C=20=C3`