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# help

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What is the inradius of a triangle with side lengths 9, 40, and 41?

Feb 29, 2020

#1
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Right scalene triangle.
Sides: a = 9   b = 40   c = 41

Area: T = 180
Perimeter: p = 90
Semiperimeter: s = 45

An incircle of a triangle is a circle which is tangent to each side. An incircle center is called incenter and has a radius named inradius. All triangles have an incenter, and it always lies inside the triangle. The incenter is the intersection of the three angle bisectors. The product of the inradius and semiperimeter (half the perimeter) of a triangle is its area.

T = rs and

r = T/s =180 / 45 = 4 - The inradius of the triangle.

Feb 29, 2020
#2
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Answer: Step-by-step explanation: From the measure of the length of the sides of the triangle, 9, 40 and 41 we can infer that the triangle is a right angled triangle. 9-40-41 is a Pythagorean triplet. In a right angled triangle, the circumradius is half the hypotenuse. In the given triangle, the hypotenuse = 41. Therefore, the circumradius is 41÷2= 20.5 units.

Feb 29, 2020