Calculate the perimeter of an isosceles triangle if the circle inscribed in the triangle divides its lateral side by a point of tangency into 4cm and 5cm segments, counting from the base.
Points D, E and K, points of tangency of the sides of the triangle with the inscribed circle, then, by the property of a tangent drawn from one point, AD = AK = 4 cm, BD = BE = 5 cm.
Then AB = AD + BD = 4 + 5 = 9 cm, and since the triangle ABC is isosceles, then BC = AB = 9 cm.
The segment EC = BC – BE = 9 – 5 = 4 cm, then, by the property of the tangent, CK = EC = 4 cm, and AC = AK + CK = 4 + 4 = 8 cm.
Let’s define the perimeter of the triangle ABC.
Ravs = AB + BC + AC = 9 + 9 + 8 = 26 cm.
Answer: The perimeter is 26 cm.
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