Question

rawn to scale
the circles: find the following

1. $x = $

Explanation:

Step1: Identify right triangle PAT

$PA$ is radius, $TA$ is tangent, so $\angle PAT = 90^\circ$.

Step2: Use cosine for $\angle ATP$

$\cos(45^\circ) = \frac{PA}{PT}$
Substitute values: $\cos(45^\circ)=\frac{\sqrt{2}}{2}$, $PT=15\sqrt{2}$, $PA=x$

Step3: Solve for $x$

$x = PT \times \cos(45^\circ)$
$x = 15\sqrt{2} \times \frac{\sqrt{2}}{2}$
$x = 15 \times \frac{2}{2} = 15$

Answer:

$15$