Answer:
[tex]RS=6\ cm[/tex]
Step-by-step explanation:
we know that
The diameter divide the circle into two equal parts
so
[tex]PR=PS[/tex]
Triangle RPO is a right triangle
Applying the Pythagorean Theorem
[tex]OR^2=RP^2+OP^2[/tex]
we have
The radius of the circle is equal to
[tex]r=10/2=5\ cm[/tex]
[tex]OP=OQ-PQ[/tex]
[tex]OQ=r=5\ cm[/tex]
[tex]PQ=1\ cm[/tex]
so
[tex]OP=5-1=4\ cm[/tex]
[tex]OR=r=5\ cm[/tex]
substitute
[tex]5^2=RP^2+4^2[/tex]
[tex]RP^2=25-16\\RP^2=9\\RP=3\ cm[/tex]
Remember that
[tex]PR=PS[/tex]
[tex]RS=2RP[/tex]
substitute
[tex]RS=2(3)=6\ cm[/tex]
