MathDB

Let

A

and

B

be points on a circle

\mathcal{C}

with center

O

such that

\angle AOB = \dfrac {\pi}2

. Circles

\mathcal{C}_1

and

\mathcal{C}_2

are internally tangent to

\mathcal{C}

A

and

B

respectively and are also externally tangent to one another. The circle

\mathcal{C}_3

lies in the interior of

\angle AOB

and it is tangent externally to

\mathcal{C}_1

\mathcal{C}_2

P

and

R

and internally tangent to

\mathcal{C}

S

. Evaluate the value of

\angle PSR

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