# Who won?

Particles $$\text{a}$$ and $$\text{b}$$ races from $$\text{ Point P}$$ to $$\text{Point Q}$$. Particle $$\text{a}$$ moves along strainght line Path A with constant velocity.

Particle $$\text{b}$$ slides down a circular Path B with horizontal component of its initial velocity equal to that of Particle $$\text{a}$$.

Let $$t_{\text{a}}$$ and $$t_{\text{b}}$$ be the time taken by Particles $$\text{a}$$ and $$\text{b}$$ to reach Q from P respectively, then

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