in the image, point a marks the center of the circle. which two lengths must form a ratio of 1:2?\na…
in the image, point a marks the center of the circle. which two lengths must form a ratio of 1:2?\na. af:ae\nb. bc:ef\nc. ef:ai\nd. ai:ef\ne. ai:ad
Answer
Explanation:
Step1: Recall the properties of a circle
In a circle, the radius is the distance from the center to any point on the circle. The diameter is twice the radius.
Step2: Analyze each option
- Option A: (AF) and (AE) are both radii of the circle. So (AF = AE), and the ratio (AF:AE=1:1).
- Option B: (BC) is a chord and (EF) is a diameter. There is no fixed (1:2) ratio between a random chord and a diameter.
- Option C: (EF) is a diameter ((EF = 2r) where (r) is the radius) and (AI) is a radius ((AI=r)). So the ratio (AI:EF=\frac{r}{2r}=\frac{1}{2}=1:2).
- Option D: (AI) is a radius and (EF) is a diameter. The ratio (AI:EF = 1:2), not (AI:EF) as written (should be (AI:EF) ratio is (1:2) but the order in the option is wrong for the ratio (1:2) as per the question's requirement of which two lengths form (1:2). Here (EF) is twice (AI), so if we want the ratio of the smaller to the larger, it's (AI:EF)).
- Option E: (AI) and (AD) are both radii. So (AI = AD), and the ratio (AI:AD = 1:1).
Answer:
C. (EF) and (AI) (since (EF) is the diameter and (AI) is the radius, and (diameter = 2\times radius), so (AI:EF=1:2))