Asked by bob

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 and the length of PR is 13 units.

Reason: Tangent segments from the same vertex to the inscribed circle are equal. So RQ = RS = 5, PQ = PU = 8, and TS = TU = 6. Hence PR = PQ + RQ = 8 + 5 = 13, and TS = TU, while the perimeter is 13 + 11 + 14 = 38 (not 19).