172. Off on a tangent


In the diagram, there are two externally tangent circles, O and O', and tangent lines l, m, n.  Lines l and n, m and n intersect at points P, Q, respectively.  Circle O has radius 4 cm and line segment PQ = 12 cm.  Also, line OO' bisects PQ.  Determine the radius of circle O'.


171. Fraction redistribution


There is a number such that, when it is subtracted from the numerator of the fraction \(\frac{5323}{7577}\) and added to the denominator, the fraction reduces to \(\frac{17}{83}\).  Determine the number.


170. Self-intersecting polygon


Determine ∠A + ∠B + ∠C – ∠D + ∠E – ∠F + ∠G + ∠H.