2014-07-28

172. Off on a tangent

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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'.

2014-07-14

171. Fraction redistribution

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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.

2014-07-01

170. Self-intersecting polygon

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