Question 823978
Because ABC is a circumscribed triangle, this means that AB, BC, and AC are tangents to the circle. Therefore, with a bit of proof (which we don't need to do really unless you want to), we can show the following is true


AP = AR
BP = BQ
CQ = CR


-------------------------------------------------------


We are given AR = 10, CQ = 8, BQ = 4, so...


AP = AR
BP = BQ
CQ = CR


turns into


AP = 10
BP = 4
8 = CR


which rearranges to


AP = 10
BP = 4
CR = 8


-------------------------------------------------------


Then we use the segment addition postulate


AB = AP + PB


AB = AP + BP


AB = 10 + 4


AB = <font color="red">14 units</font>