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horsena [70]
3 years ago
11

Can someone please explain how to solve this problem(31)

Mathematics
1 answer:
pogonyaev3 years ago
4 0

Answer:

  (-1.92, 1.08)

Step-by-step explanation:

The <em>incenter</em> is the center of the largest circle that can be inscribed in the triangle. That circle is called the <em>incircle</em>. The incenter is at the point of intersection of the angle bisectors. For a right triangle, the <em>inradius</em> (the radius of the incircle), is found from a simple formula:

  r = (a + b - c)/2 . . . . . where c is the hypotenuse, and a and b are the legs

In your triangle, the inradius is ...

  r = (5 + 3 -√(5² +3²))/2 = 4 -√8.5 ≈ 1.08452

Among other things, this means the coordinates of the incenter are about (1.08, 1.08) from the right angle vertex, so are about ...

  incenter ≈ (-1.92, 1.08)

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