In an isosceles triangle, the center of the inscribed circle divides the height
| August 19, 2021 | education
In an isosceles triangle, the center of the inscribed circle divides the height by a ratio of 17: 15, and the side is 34 cm. Find the base of the triangle.
The center of a circle inscribed in a triangle is the intersection point of the bisectors.
ОА is the bisector of the angle BAC.
By the property of the bisector, it divided the opposite side into segments proportional to the adjacent sides.
AB / OB = AH / OH.
AH = AB * OH / OB = 34 * 15/17 = 30 cm.
The bisector BH drawn to the base of the isosceles triangle ABC is also its median, then CH = AH = 30 cm.
AC = AH + CH = 30 + 30 = 60 cm.
Answer: The length of the base is 60 cm.
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