In triangle FKE, KF = EF. Calculate the perimeter of triangle FKE.

Analysis:

• The image shows a triangle FKE with an inscribed circle.
• O is the center of the inscribed circle.
• Points of tangency are shown on the sides. Let's label them:
• Let the point of tangency on FK be M.
• Let the point of tangency on KE be the vertex E itself, which would imply KE is tangent at E, which is not possible for an inscribed circle unless KE is a point. This indicates an error in interpreting the diagram.
• Let's assume the labels 8 and 6 refer to segment lengths from the vertices to the points of tangency.

The problem states KF = EF. This means triangle FKE is an isosceles triangle with the base KE.

Looking at the diagram again:

• Side FK has a length labeled 8.
• Side KE has a length labeled 6.
• Side EF has a length labeled 8.

This means FK = 8, KE = 6, and EF = 8. The condition KF = EF is satisfied (8 = 8).

The perimeter of triangle FKE is the sum of its side lengths:

Perimeter = FK + KE + EF

Perimeter = 8 + 6 + 8 = 22.

Ответ: 22