segment BC is tangent to circle A at B

Question

and to circle D at C. (Not drawn to scale) AB=10 BC=25 and DC=3. Find AD to the nearest tenth. Hint: Draw an auxiliary line from D to segment BA.

{There are two circles, the larger one has point A in the center and a dotted line going up to the top of the circle which goes to point B at the top of the circle. There is a diagonal line to the top of the smaller circle. The point at the top of the smaller circle is point C, and the center of that circle is D}

26
28.2
25.2
26.9

I'm sorry I can't get a picture linked, but I hope the description should help. I really appreciate your help! THank you!

Answer 1

I think I got the diagram done.
Following their hint to draw a line from D to AB ....
draw the line to hit AB at 90° at a point E.

We know that in a circle, the radius meets the tangent at 90°, so the angles at B and C are each 90°
so BEDC is a rectangle, making ED = 25

So triangle ADE is right-angled , with AD the hypotenuse and AE = 7

AD^2 = 25^2 + 7^2 = 674
AD =√674 = appr 25.96

So what do you think is the correct choice?

Answer 2

Thank you so much! :D