Problem 6.
A circle is inscribed in a right triangle with dimensions x, y, and r
(x and y are the distances from the corners to where the circle intersects the legs and r is the radius of the circle) as shown below.
Find the area of the triangle in terms of x and y only (without r).


Solution:

Let A be the area of the triangle.

Express twice the area in two different ways:

(1) Use the formula for twice a triangle: 2A = base * height


(2) Add the components to form the area of the rectangle with dimensions
(y+r) and (x+r):


Therefore,


Notice that the left side of the last equation is half the right side of the equation
and is therefore the area of the triangle.



| Problem 1 | Problem 2 | Problem 3 | Problem 4 | Problem 5 |
| Problem 6 | Problem 7 | Problem 8 | Problem 9 | Problem 10 |

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