Question

qr is tangent to circle p at point q. what is the approximate length of rp? round to the nearest tenth. 5.3 3 r p 5.6 units 6.1 units 8.3 units 9.8 units

Explanation:

Step1: Identify right triangle property

A tangent to a circle forms a right angle with the radius at the point of tangency, so $\triangle QRP$ is a right triangle with $\angle Q = 90^\circ$.

Step2: Apply Pythagorean theorem

For right triangle $\triangle QRP$, $RP^2 = QR^2 + QP^2$. Substitute $QR=5.3$, $QP=3$:
$RP^2 = 5.3^2 + 3^2$

Step3: Calculate squared values

$5.3^2 = 28.09$, $3^2 = 9$, so $RP^2 = 28.09 + 9 = 37.09$

Step4: Solve for RP

Take square root: $RP = \sqrt{37.09} \approx 6.1$

Answer:

6.1 units