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 si
des 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.
2 answers:
Answer:
<u>The true statements are:</u>
TU ≅ TS
The length of line segment PR is 13 units.
Step-by-step explanation:
See the attached figure.
As shown, The circle is inscribed in triangle PRT.
There are 2 segments tangents to the circle from point P ⇒ PQ , PU
There are 2 segments tangents to the circle from point R ⇒ RQ , RS
There are 2 segments tangents to the circle from point T ⇒ TS , TU
The length of RS is 5, the length of PU is 8, and the length of UT is 6.
So, RS = RQ = 5 , PU = PQ = 8 , TU = TS = 6
We will check the options:
(1) The perimeter of the triangle is 19 units. ⇒ Wrong
Because: The perimeter of the triangle is 38 units.
The perimeter of the triangle = PR+RT+TP = (PQ+QR)+(RS+ST)+(TU+UP)=38
(2) TU ≅ TS ⇒ True
Because: TS , TU are tangents to the circle from point T
(3) PU ≅ TU ⇒ Wrong
Because: PU = 8 and TU = 6
(4) The length of line segment PR is 13 units. ⇒ True
Because: PR = PQ + QR = 8 + 5 = 13 units
(5) The length of line segment TR is 10 units. ⇒ Wrong
Because: TR = TS + SR = 6 + 5 = 11
<u>The true statements are:</u>
TU ≅ TS
The length of line segment PR is 13 units.
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