Question

in the image, point a marks the center of the circle. which two lengths must form a ratio of 1:2? a. af:ae b. bc:ef c. ef:ai d. ai:ef e. ai:ad

Explanation:

Step1: Identify circle properties

Point $A$ is the center, so $AF, AE, AI, AD$ are radii: $AF=AE=AI=AD$.

Step2: Analyze each option

• A. $AF:AE = 1:1$ (equal radii, not 1:2)
• B. $BC:EF$: No fixed 1:2 relation (chords depend on arcs)
• C. $EF:AI$: $EF$ is a diameter ($2\times$ radius), $AI$ is radius. So $EF:AI = 2:1$ (reverse of 1:2)
• D. $AI:EF$: $AI$ is radius, $EF$ is diameter ($EF=2\times AI$). So $AI:EF = 1:2$
• E. $AI:AD = 1:1$ (equal radii, not 1:2)

Answer:

D. AI:EF