Doubt from conics

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I m getting B

Given answer is D bro

Here ΔAPS_2 \approx ΔAS_1P

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I got \frac{1}{√3}

one doubt bro, why should "P" line on a circle for the angle S1PS2 to be maximum, can you elaborate it, bro can't we take point on the line joining S1 and S2(between them ) for the max angle?

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For the max angle the line must be tangent to the circle
Also see yourself by displacing p along the line

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For this question
S_1P<S_2P \implies \frac{S_1P}{S_2P}<1 Good for MCQ. @Venkat_2020

Thanks for you solution bro @Satyendra_2019

But , Bro I didn't get why should the point be the point of contact of tangent ,what is the reason bro?

Bro try other P''part you will get it