Question

qr is tangent to circle p at point q. what is the approximate length of rp? round to the nearest tenth. 5.6 units 6.1 units 8.3 units 9.8 units

Explanation:

Step1: Recall tangent - radius property

A tangent to a circle is perpendicular to the radius at the point of tangency. So, $\triangle PQR$ is a right - triangle with $\angle PQR = 90^{\circ}$.

Step2: Apply the Pythagorean theorem

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

Step3: Calculate the value of $RP$

First, calculate $5.3^{2}=28.09$ and $3^{2}=9$. Then $RP=\sqrt{28.09 + 9}=\sqrt{37.09}\approx6.1$.

Answer:

6.1 units