CEMC Fryer, 2007

Geometry Difficulty 2.0 Junior Prove it Canada

To reduce the total length of rope used, rope $HC$ and rope $HD$ are to be replaced by a single rope $HP$ where $P$ is a point on the straight line between $C$ and $D$ . (The balloon remains at the same position $H$ above $O$ as in part (b).) Determine the greatest length of rope that can be saved. Explain how you obtained your answer.

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