How do I solve this geometry problem?

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10)
Since angle RQP = 90º, and since all three points lie on the edge of a circle, it forms an inscribed angle.
For inscribed angles, the intercepted arc equals double the inscribed angle.
Since arc RSP is the intercepted arc for the inscribed angle RQP, then arc RSP = 2 * 90º = 180º
And because arc RSP = 180º which is half of a circle, then arc RQP must equal 180º.
Since arc RQP is the intercepted arc for inscribed angle RSP, then angle RSP = (1/2)(180) = 90º
If we drew a line from R to P, we would form two right triangles. Triangle RSP is one and triangle RQP is the other.
We calculate the length of RP for triangle RQP by using the Pythagorean Theorem as follows
(RP)^2 = (QR)^2 + (PQ)^2
(RP)^2 = (20)^2 + (15)^2
(RP)^2 = 400 + 225
(RP)^2 = 625
RP = 25
Finally, we calculate the length of PS for triangle RSP by using the Pythagorean Theorem as follows
(RP)^2 = (RS)^2 + (PS)^2
(25)^2 = (7)^2 + (PS)^2
625 = 49 + (PS)^2
576 = (PS)^2
24 = PS

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