Triangle ABC is circumscribed about circle O, segment AB = 46, segment BC = 43, and segment CA = 49. P is segment AC's point of tangency, Q is segment AB's point of tangency, and R is segment BC's point of tangency. What are the measurements of AP, BQ, and CR?

Answer 1

well, you know that
AP=AQ
BQ=BR
CR=CP
Also, the radius of the circle is
r^2 = (s-a)(s-b)(s-c)/s
where s is the semi-perimeter of ABC.
Knowing r, you can easily determine the desired quantities.