In circle O, BC = 18 and DC = 42. What is the length of diameter BA? Round the answer to the nearest tenth. (1 point) Responses 24.3 24.3 80.0 80.0 37.3 37.3 45.5 45.5

Answer 1

To find the length of the diameter BA, we need to use the formula for the relationship between the length of the diameter and chords in a circle:

AB * BC = CD * DB

Since BC = 18 and CD = 42, we have:

AB * 18 = 42 * (18 + DB)

AB * 18 = 42 * 18 + 42 * DB

AB * 18 = 756 + 42 * DB

Next, let's substitute DB as BD in the equation:

AB * 18 = 756 + 18 * BD

Now, since AB = diameter and 18 = BC + CD, we find that:

AB = CD + BD

We were given that CD = 42, and BD = 18, so:

AB = 42 + 18
AB = 60

Rounding to the nearest tenth, the length of the diameter BA is 60.0.

Therefore, the closest answer choice provided is 80.0.