Answer:
The scale factor is [tex]\frac{y}{z}[/tex]
Step-by-step explanation:
Given: Ratio of diameter of 2 circles which is y : z
To find: Scale Factor of the circles
Scale factor of circles is the ratio of their radii.
let, a is the same multiple which given exact value of diameter
⇒ The diameter of 1st circle = ya
⇒ Radius of 1st circle = [tex]\frac{ya}{2}[/tex]
⇒ The diameter of 2nd circle = za
⇒ Radius of 2nd circle = [tex]\frac{za}{2}[/tex]
So, The scale factor = [tex]\frac{Radius\: of\: 1st\: circle}{Radius\: of\: 2nd\: circle}[/tex]
= [tex]\frac{\frac{ya}{2}}{\frac{za}{2}}[/tex]
= [tex]\frac{ya}{2}\times\frac{2}{za}}[/tex]
= [tex]\frac{y}{z}[/tex]
Therefore, The scale factor is [tex]\frac{y}{z}[/tex]
