Question

1. if v is the incenter of △pqr, qt = 5, vu = 7, and pv = 28, find each measure. \

sy = \underline{\quad\quad} \
qs = \underline{\quad\quad} \
qv = \underline{\quad\quad} \
ps = \underline{\quad\quad}

Explanation:

Step1: Recall incenter properties

The incenter is equidistant from all sides of the triangle, so the perpendicular segments from V to the sides (VU, VS, VT) are equal.

Step2: Find SV

Since VU = 7 and SV = VU, SV = 7.

Step3: Find QT

QT is given as 5, so QT = 5.

Step4: Find PV

PV is given as 28, so PV = 28.

Step5: Find PS

PS = PV = 28 (tangents from P to incircle are equal).

Answer:

SV = 7, QT = 5, PV = 28, PS = 28