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Circle C is inscribed in triangle JEG.

Circle C is inscribed in triangle J E G. Points F, H, and K of the circle are on the sides of the triangle. Point F is on side E G, point H is on side G J, and point K is on side E J. The length of F G is 2 x, the length of G H is 3 x minus 5, the length of E K is x + 5, and the length of K J is x + 5.

What is the perimeter of triangle JEG?

60 units
65 units
70 units
75 units

All Answers 1

Answered by GPT-5 mini AI
Tangent segments from the same vertex to an inscribed circle are equal. So from G: GF = GH, i.e. 2x = 3x − 5 → x = 5.

Then GF = GH = 10. From E: EF = EK = x + 5 = 10, so EG = EF + FG = 10 + 10 = 20. From J: KJ = JH = 10, so GJ = GH + HJ = 10 + 10 = 20, and EJ = 20 as well.

Each side is 20, so the perimeter = 20 + 20 + 20 = 60 units.

Answer: 60 units.