In a right triangle ABC, right angled at B, BC=12 cm and AB=5CM. The radius of the circle inscribed in the triangle (in cm) is
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AC can be calculated by Pythagoras' theorem as 13 cm. Now construct the circle whose radius is to be found.
Joint its center to the vertices of the triangle. Also construct each of the radii at the points where the sides of the triangle are tangent to the circle.
We can find three smaller triangles inside the original one now with base as one of the sides of the triangle. All of them have the same altitude i.e. the radius of the circle. So each of them has area (1/2)*Side of triangle*radius of circle.
Their combined area gives us the area of the triangle. So (1/2)*(Perimeter of triangle)*radius = area of the original triangle.
But the area of the larger triangle is also given by 1/2*Product of legs. So Putting both the formulas together, (5+12+13)*r = 5*12. This gives r = 2 cm where r is the radius of the circle inscribed in the 5-12-13 triangle.
Joint its center to the vertices of the triangle. Also construct each of the radii at the points where the sides of the triangle are tangent to the circle.
We can find three smaller triangles inside the original one now with base as one of the sides of the triangle. All of them have the same altitude i.e. the radius of the circle. So each of them has area (1/2)*Side of triangle*radius of circle.
Their combined area gives us the area of the triangle. So (1/2)*(Perimeter of triangle)*radius = area of the original triangle.
But the area of the larger triangle is also given by 1/2*Product of legs. So Putting both the formulas together, (5+12+13)*r = 5*12. This gives r = 2 cm where r is the radius of the circle inscribed in the 5-12-13 triangle.
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