SOLUTION: A circle is inscribed in a triangle with sides of lengths 3 cm, 4 cm, and 5 cm. The radius of this circle, in cm, is:
(A) 5/7 (B) 1 (C) 7/5 (D) 2 (E) none of these
Algebra.Com
Question 280082: A circle is inscribed in a triangle with sides of lengths 3 cm, 4 cm, and 5 cm. The radius of this circle, in cm, is:
(A) 5/7 (B) 1 (C) 7/5 (D) 2 (E) none of these
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
r = sqrt [(s - a)(s - b)(s - c)/s] where s = (a + b + c)/2
-----------
s = (3+4+5)/2 = 6
r = sqrt(3*2*1/6)
r = 1 cm
------------
This is very similar to Heron's Law for the area of a triangle, the difference being that "s" inside the radical is a divisor rather than a multiplier.
It works for all triangles, not just right triangles.
RELATED QUESTIONS
PQR is an isosceles triangle with a base of 18 cm and sides of 15 cm and is inscribed in... (answered by ikleyn,ankor@dixie-net.com)
A triangle with sides of length 36 cm, 77 cm, and 85 cm are inscribed in a circle. Inside (answered by ikleyn)
A circle passes through the vertices of a triangle with sides of length 3.3 cm, 5.6 cm... (answered by math_tutor2020)
A circle passes through the vertices of a triangle with sides of length 3.3 cm, 5.6 cm... (answered by ikleyn)
A rectangle is inscribed in a circle of radius 6.5 cm. If the the length of the rectangle (answered by mananth)
A right triangle is inscribed in a circle of radius 7.5 cm. One of its sides is 15 cm... (answered by ankor@dixie-net.com,KMST)
An equilateral triangle is inscribed in a circle of a radius 6 cm., find its side
(answered by josgarithmetic)
A right triangle is inscribed in a circle with radius 26 cm. If the length of one of the... (answered by ikleyn)
Equilateral triangle ABC has sides of 22 cm. A circle of radius 5 cm inside it is tangent (answered by greenestamps)