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 8.3 units 9.8 units 6.1 units

Explanation:

Step1: Recall tangent - radius property

Since 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 $QP=3$. So $RP=\sqrt{5.3^{2}+3^{2}}=\sqrt{28.09 + 9}=\sqrt{37.09}\approx6.1$.

Answer:

6.1 units