Analysis of Geometrical Figures and Expressions:
- Figure 1: This figure shows a triangle ABC with an inscribed circle. The points where the circle touches the sides are labeled E, F, and implicitly another point on BC. The lengths of segments from the vertices to the points of tangency are given or implied: AE = 4, BE = 10, CF = 6. The question asks for 'P_{ABC}-?', which likely means the perimeter of triangle ABC. The perimeter can be calculated by summing the lengths of the sides. Since the lengths from a vertex to the points of tangency of the incircle are equal, we have AE = AF = 4, BE = BD = 10, and CF = CD = 6. Thus, the sides are AB = AE + EB = 4 + 10 = 14, BC = BD + DC = 10 + 6 = 16, and AC = AF + FC = 4 + 6 = 10. The perimeter P_{ABC} = AB + BC + AC = 14 + 16 + 10 = 40.
- Figure 2: This figure depicts a circle with center O and an inscribed triangle ABC. An angle AOC is indicated, and an angle within the triangle, labeled 40 degrees, appears to be angle BAC. The question associated with this figure is '
- Figure 3: This figure shows a circle with center O, tangent to a line at point C. Point A is marked on the tangent line. The expression 'AC-касательная' confirms that AC is a tangent. The question asks for '
- General Mathematical Expressions:
- 'P_{ABC}-?': As analyzed in Figure 1, this asks for the perimeter of triangle ABC.
- '
- 'AC-касательная': This states that AC is a tangent line.
- '
- '
Note: The figures and their associated questions seem to be from different problems or parts of a larger problem set. The numbers and angles provided need careful interpretation within each specific context.