To find the length of AD, we can use the tangent-secant theorem: when a line is tangent to a circle and a secant line from the external point to the circle intersect, the square of the length of the tangent segment is equal to the product of the lengths of the entire secant segment and the external secant segment.
In this case, BC is tangent to circle A at B and to circle D at C. Therefore, we have:
BC^2 = AD * DC
Substitute the length of BC (19) into the equation:
19^2 = AD * DC
361 = AD * DC
Since we don't know the length of DC, we can't solve for AD exactly. However, we know that BC = AD + DC. Given that BC is 19, and this is tangent to both circles A and D, we can rearrange the equation to find that AD = 19 - DC.
With this information, let's look at the answer choices:
20.2: AD = 19 - 20.2 = -1.2, negative value which doesn't make sense
25.5: AD = 19 - 25.5 = -6.5, negative value which doesn't make sense
19.2: AD = 19 - 19.2 = -0.2, negative value which doesn't make sense
21.5: AD = 19 - 21.5 = -2.5, negative value which doesn't make sense
Therefore, the correct answer is none of the given options. Sorry for the confusion.
BC=19
BC is tangent to circle A at B and to circle D at C. What is AD to the nearest tenth?
20.2
25.5
19.2
21.5
1 answer