Calculate the radius of the circle that is inscribed in triangle ABC whose sides are 3,4,5.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We notice that if we'll add the squares of the lengths of 2 sides of the triangle ABC, we'll get the square of the biggest one.

5^2 = 3^2 + 4^2

 25 = 9 + 16

25 = 25

This equality certifies the fact that the triangle ABC is a right angled triangle, whose right angle is A = 90 degrees.

The opposite side to the right angle A is called hypothenuse, BC.

The hypothenuse represents the diameter of the circle and we'll get:

R = hypotenuse/2

Since hypotenuse is the biggest side of a right angle triangle, that means that BC = 5.

R = 5/2

The radius of the inscribed circle in the given triangle is:

r = S/p

S = AB*AC/2

S = 3*4/2

S = 6 square units (area of the triangle ABC)

p = (3+4+5)/2

p = 12/2

p = 6 units

r = 6 square units/ 6 units

r = 1 unit.

The radius of the inscribed circle is r = 1 unit.

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