Bc is tangent to circle a at b and to circle d at c. what is ad to the nearest tenth? look at image attached.

1. 19.2

Step-by-step explanation:    

Please find the attachment.

Since we know that radius is perpendicular to tangent of a circle. So AB will be perpendicular to BC at c and DC is perpendicular to CB at C.

Now we will construct a perpendicular line to radius AB at point E from the center of our small circle. Since we have two right angles at point B and C so we will also have right angles at point E and D as well.    

Length of CD is is 7 so length of BE will be 7 as well and length of EA will be 10-7=3. Length of DE will be equal to length BC that is 19.

Now we have formed a right triangle and now we will use Pythagoras theorem to find the length of AD.  

Upon substituting our values in above formula we will get,

Upon taking square root of both sides of our equation we will get,

Therefore, the length of AD will be 19.2 and 1st option is the correct choice.

b. astronomers