Geometry problem
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The document shows how to calculate the radius of a circle inscribed in a right triangle given the lengths of the two legs. It uses the Pythagorean theorem to find the hypotenuse is 13 units. It then calculates the semi-perimeter and area of the triangle. The radius of the inscribed circle is the area divided by the semi-perimeter, which is 2 units.
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Geometry problem
- 1. What is the radius of a circle inscribed in a right triangle with legs of 5 units and 12 units? r² = x² + y² r² = 5² + 12² r = 13 unit length half of perimeter of triangle is s = ½ (5 + 12 + 13) = 15 unit length and area of triangle is L = ½ x y = ½ (5)(12) = 30 unit area Let R is radius of a circle inscribed in a right triangle, so... R = L/s = 30/15 = 2 unit length