Question

$\overline{qr}$ is a tangent to $\odot$t.
true
false

Explanation:

Step1: Calculate length of TR

$TR = TS + SR = 8 + 22 = 30$

Step2: Check Pythagorean theorem

If $QR$ is tangent, $\triangle TQR$ is right-angled at $Q$, so $TQ^2 + QR^2$ should equal $TR^2$.
Calculate $TQ^2 + QR^2 = 8^2 + 17^2 = 64 + 289 = 353$
Calculate $TR^2 = 30^2 = 900$

Step3: Compare the two values

$353
eq 900$, so the triangle is not right-angled.

Answer:

False