find-the-radius-of-a-circle-wich-inscribes-an-equalateral-triangle-with-perimeter-of-24cm-

Question Number 33317 by mondodotto@gmail.com last updated on 14/Apr/18

find the radius of a circle

wich inscribes an equalateral triangle

with perimeter of 24 cm

Answered by MJS last updated on 14/Apr/18

I^{'} m not sure if you mean the

circumcircle or the inscribed

circle (my english might not be

good enough)

equilateral triangle a = b = c

perimeter = a + b + c = 3 a = 24

a = 8

in an equilateral triangle the

radius of the circumcircle

R = \frac{2}{3} h and the radius of the

inscribed circle is r = \frac{1}{3} \Rightarrow R = 2 r

a^{2} = h^{2} + {(\frac{a}{2})}^{2}

h = \sqrt{a^{2} - \frac{a^{2}}{4}} = \sqrt{\frac{3 a^{2}}{4}} = a \frac{\sqrt{3}}{2}

R = a \frac{\sqrt{3}}{3} = \frac{8 \sqrt{3}}{3} \approx 4.62

r = a \frac{\sqrt{3}}{6} = \frac{4 \sqrt{3}}{3} \approx 2.31

Commented by mondodotto@gmail.com last updated on 15/Apr/18

sure sir thats what i meant thanks for your help