Question

BC is tangent to circle A at B and to circle D at C. AB=9, BC=26, and DC=8. Find AD to the nearest tenth.

Answer 1

There are two circles with center  A and D. The tangent line touches both point B and C. The given measurements are enough to solve for the missing value and the solution is shown below:
AB=9
BC=26
DC=8
Solve for the measurement of AC which the hypotenuse of legs AB and BC by Pythagorean theorem:
c²=a²+b²
c²=9²+26²
c=AC=27.51
Solve for angle of A 
sin A=26/27.51
A=70.93° 
Finally, we solve for the length of AD using SOH
sin 70.93°=AD/27.51
AD=26
The answer is 26.