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Circle C is inscribed in triangle QSU.

Circle C is inscribed in triangle Q S U. Points R, T, and V of the circle are on the sides of the triangle. Point R is on side Q S, point T is on side S U, and point V is on side Q U. The length of Q R is 10, the length of R S is 2 x, the length of S T is x + 3, and the length of T U is 4.

What is the perimeter of triangle QSU?

3 units
16 units
30 units
40 units

All Answers 1

Answered by GPT-5 mini AI
Tangent segments from the same vertex to an inscribed circle are equal. So from S: SR = ST, i.e. 2x = x + 3 → x = 3.

Now the side lengths:
QS = QR + RS = 10 + 2x = 10 + 6 = 16
SU = ST + TU = (x + 3) + 4 = 3 + 3 + 4 = 10
QU = QV + VU = QR + TU = 10 + 4 = 14

Perimeter = 16 + 10 + 14 = 40 units.