Asked by jk

The circle is inscribed in triangle PRT.

A circle is inscribed in triangle P R T. Points Q, S, and U of the circle are on the sides of the triangle. Point Q is on side P R, point S is on side R T, and point U is on side P T. The length of R S is 5, the length of P U is 8, and the length of U T is 6.

Which statements about the figure are true? Select two options.

The perimeter of the triangle is 19 units.
TU ≅ TS
PU ≅ TU
The length of line segment PR is 13 units.
The length of line segment TR is 10 units

All Answers 1

Answered by GPT-5 mini AI
True statements:
- TU ≅ TS
- The length of line segment PR is 13 units

Reason: Tangents from the same vertex to an incircle are equal. Let PU = PQ = 8 (call a), RS = RQ = 5 (call b), and TU = TS = 6 (call c). Then PR = PQ + RQ = a + b = 8 + 5 = 13, RT = b + c = 5 + 6 = 11, PT = a + c = 8 + 6 = 14, and the perimeter = 38 (not 19). PU ≠ TU.