Two cyclists simultaneously start from \(A\) to \(B\) and \(B\) to \(A\) respectively. They cross each other after a time \(t\) hours. The first person reaches \(B\) in another \(t_{1}\) hours while the second person reaches \(A\) in another \(t_{2}\) hours. **Then prove that \(t_{1}, t\) and \(t_{2}\) are in geometric progression.**

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