Question

Найди длину высоты треугольника OAB, опущенную на сторону АВ, если периметр треугольника ОНВ составляет 24 см, а диматер изображенной окружности равен 20 см, АВ = 12 см.

Answer 1

The height of triangle OAB is 8 cm

Explanation:

The question in English is

Find the length of the height of the triangle OAB dropped to the side of AB, if the perimeter of the triangle OHV is 24 cm, and the diameter of the circle shown is 20 cm, AB = 12 cm.

The picture of the question in the attached figure

we know that

If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc

In this problem the diameter of the circle CD is perpendicular to the chord AB, that means that the diameter bisect the chord

so

`AH=HB`

`HB=(AB)/(2)=(12)/(2)=6\ cm`

Remember that the perimeter of triangle is equal to the sum of its three length sides

so

Perimeter of triangle OHB is given by

`P=OH+HB+OB`

we have

`P=24\ cm`

`HB=6\ cm`

`OB=r=20/2=10\ cm` ---> the radius is half the diameter

substitute the given values

`24=OH+6+10`

solve for OH

`24=OH+16\\OH=24-16\\OH=8\ cm`

therefore

The height of triangle OAB is 8 cm