Given a Circle Inscribed in a Triangle, Find the Radius of the Circle.

To find the radius, I use two different formulas for the area of a triangle.

[@LawoftheCosines]

the circle is called the incircle and the radius, inradius

[@carolynzhou6708]

Love It! Thank you for helping me solve my homework! Life just became much simpler!

[@TheMathDistrict]

Thank you, I'm happy to hear that!

[@jaimeyomayuza6140]

Excelente explicación gracias por su tiempo y dedicación.
From Bogota D.C

[@bkp_s]

Good lesson mam. Thanks a lot

[@TheMathDistrict]

It's my pleasure.

[@Grizzly01]

Exact form: r = (√231)/6

[@user-vm1im1jc6j]

Like √8*9*10/ 6 ?

[@melvynnesperosvlog32]

How do you get 231 and 6?

[@mikhaCatlovers]

I got the same answer 😅

[@someonespadre]

Found the formula in the back of my copy Major-General Shortrede’s logarithmic Trig Function Tables (19th century). Didn’t know it’s called Heron’s formula. Shortrede uses it thus: SinA=(2/b*c)*area.

[@manalthangam]

Nice one after long gap.
Many thanks Madam!

[@richardbailey2001]

Heron's formula is one for the book for future reference, thank you!

[@repsaknivek]

Hmm. so the answer turns out to be the triangle's area divided by S (the semi-perimeter of the triangle). Is it always that way? Because then we could solve for the radius in just a few seconds each time.

[@sethstuff921]

Amazing solution, keep it up!

[@Soh965]

Ingenious...

[@footballCartoon91]

this is the first time i heard about that heron's formula. This algorithm is good for finding the maximum radius of a circle in a given triangle. I think. But square root in programming is quite slow.

[@footballCartoon91]

for anyone interested to implemented this in code, you can find r by:
r=2*total_triangle_area/|AC|+|AB|+|BC|

[@fhffhff]

S=9*231^0.5/4 r=231^0.5/6

[@admnner21111]

Tnx!❤

[@claudeabraham2347]

Very good!

[@omnigod7624]

Is there any shorter method?

[@poornimadabekar4764]

😂

[@omnigod7624]

I mean it's not hard and I can easily do it but it's too lengthy

[@drwzer]

After finding area of triangle using heron’s equation, you can use a simple equation: area of triangle equal to semi perimeter times radius.

[@chrisreed5463]

​@@drwzerThat’s what GPT4 does.