Answer:
"The length of the line segment PR is 13 units" and TU=TS
Explanation:
"The perimeter of the triangle is 19 units"
False - if you add up the marked measurements (8,6, and 5), you already get 19, so the perimeter is more than 19 units.
TU=TS
Call the centre of the circle C.
TC=TC
UC=SC (radius)
∠TCU=∠SCT (TC bisects ∠UCS)
∴ΔTUC is congruent to ΔTCS
∴TU=TS=6, TRUE
PU=TU
False - PU=8, TU=6, 8≠6
"The length of the line segment PR is 13 units"
ΔRQC=ΔRSC (QC=SC, RC=RC, ∠QSC=∠CRS)
∴RS=RQ=5
ΔPUC=ΔPQC (UC=QC, PC=PC, ∠UPC=∠CPQ)
∴PU=PQ=8
PR=PQ+QR=8+5=13, TRUE
"The length of the segment TR is 10 units"
False
ΔTSC=ΔTUC (UC=SC,TC=TC,∠UCT=∠SCT)
∴TU=TS=6
TR=TS+SR=6+5=11