Question

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.

Answer 1

Answer: b and e

Step-by-step explanation:

Answer 2

Option B:
`TU $\cong$ TS PU $\cong$ TU`

Option C: The length of line segment PR is 13 units.

Step-by-step explanation:

Given that the circle is inscribed in triangle PRT. 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 RS is 5, the length of PU is 8 and the length of UT is 6.

Option A: The perimeter of the triangle is 19 units.

The perimeter of the triangle is given by

Perimeter of ΔPRT = PU + UT + TS + SR + RQ + QP

Since, P, T and R are tangents to the circle and we know that "Tangents to a circle drawn to a point outside the circle are equal in length".

Thus, we have,

RS = RQ = 5

PU = PQ = 8 and

UT = TS = 6

Substituting the values in the perimeter of ΔPRT, we get,

Perimeter of ΔPRT = 8 + 6 + 6 + 5 + 5 + 8 =38 units

Thus, the perimeter of the triangle is 38 units.

Hence, Option A is not the correct answer.

Option B :
`TU $\cong$ TS PU $\cong$ TU`

Since, P, T and R are tangents to the circle and we know that "Tangents to a circle drawn to a point outside the circle are equal in length".

Then
`TU $\cong$ TS PU $\cong$ TU`

Hence, Option B is the correct answer.

Option C: The length of line segment PR is 13 units.

The length of PR is given by

PR = PQ + QR

Substituting the values RQ = 5 and PQ = 8, we get,

PR = 5 + 8 = 13 units

Thus, the length of line segment PR is 13 units.

Hence, Option C is the correct answer.

Option D: The length of line segment TR is 10 units.

The length of TR is given by

TR = TS + SR

Substituting the values TS = 6 and SR = 5, we get,

TR = 6 + 5 = 11 units

Thus, the length of line segment TR is 11 units

Hence, Option D is not the correct answer.