The triangle MCP is isosceles, its perimeter is 66 m and the base of MС is 26 m. Find the lengths of the line segments

| July 17, 2021 | education

The triangle MCP is isosceles, its perimeter is 66 m and the base of MС is 26 m. Find the lengths of the line segments AM and AP (A-point of tangency of the inscribed circle with side MP.

From the vertex P of the triangle, we omit the height PH, which is also the median in an isosceles triangle, divides the base into two equal segments MH = CH = MC / 2 = 26/2 = 13 cm.

The segments MA and MH are equal as tangents to the circle drawn from one point. MA = MH = 13 cm.

Knowing the perimeter of the triangle and the length of its base, we determine the lengths of the sides of the triangle.

P = 2 * MP + MC.

66 = 2 * MP + 26.

2 * MR = 40 cm.

MP = 40/2 = 20 cm.

Then the segment AP = MP – MA = 20 – 13 = 7 cm.

Answer: The length of the segment AM is 13 cm, the segment AP is 7 cm.



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