qr is tangent to circle p at point q. what is the approximate length of rp? round to the nearest tenth. 5.6…

Answer:

C. 6.1 units

Explanation:

Step1: Recall tangent - radius property

Since $\overline{QR}$ is tangent to circle $P$ at point $Q$, then $\angle PQR = 90^{\circ}$ (a tangent to a circle is perpendicular to the radius at the point of tangency).

Step2: Apply Pythagorean theorem

In right - triangle $PQR$, by the Pythagorean theorem $RP^{2}=QR^{2}+QP^{2}$. Given $QR = 5.3$ and $QP = 3$. Then $RP=\sqrt{5.3^{2}+3^{2}}=\sqrt{28.09 + 9}=\sqrt{37.09}\approx6.1$.