Answer: [tex]6.1\text{ units}[/tex]
Step-by-step explanation:
Given: Tangent [tex]\overline{QR}[/tex] is tangent to circle P at point Q.
We know that the radius from the center of the circle to the point of tangency is perpendicular to the tangent line.
Therefore,Tangent [tex]\overline{QR}[/tex] is perpendicular to radius QP at point of tangency Q.
Then, the triangle formed by Tangent and radius must be aright triangle.
So by Pythagoras theorem, we have
[tex]\overline{RP}^2=\overline{RQ}^2+\overline{QP}^2\\\\\Rightarrow\overline{RP}^2=(5.3)^2+(3)^2\\\\\Rightarrow\overline{RP}^2=37.09\\\\\Rightarrow\overline{RP}=\sqrt{37.09}=6.09015599143\approx6.1\text{ units}[/tex]
Hence, the approximate length of [tex]\overline{RP}=6.1\text{ units}[/tex]
