In circle O, BC = 18 and DC = 42. The diagram is not drawn to scale.
A circle with center O and points D, B, and A is shown. Point C is located outside of the circle. Line CBA extends out from the circle. Line CD extends outside of the circle.
What is the length of diameter BA? Round the answer to the nearest tenth.
(1 point)
Responses
37.3
45.5
80
24.3
To find the length of diameter BA, we can use the Pythagorean theorem as follows:
OD^2 + BD^2 = OB^2
Since BD = BC + CD = 18 + 42 = 60, and OD = OB (radius), let's denote OB as x:
x^2 + 60^2 = (2x)^2
x^2 + 3600 = 4x^2
3600 = 4x^2 - x^2
3600 = 3x^2
x^2 = 3600 / 3
x^2 = 1200
x = √1200
x ≈ 34.6
Thus, the length of diameter BA ≈ 2x ≈ 2 * 34.6 ≈ 69.2
Rounded to the nearest tenth, the length of the diameter BA is 69.2.
Therefore, none of the answer options provided exactly matches the calculated length, so the best answer would be to choose 69.2 (even though it's not listed).