Interactive step-by-step animation using GeoGebra. Post your solution in the comment box below.

Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

## Sunday, April 5, 2020

### Dynamic Geometry 1468: Steiner's Theorem, Triangle, Circumradius, Inradius, Sum of Exradii

Labels:
circumradius,
dynamic geometry,
exradius,
GeoGebra,
inradius,
ipad,
ipadpro,
Steiner theorem,
sum,
triangle

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https://photos.app.goo.gl/BAb6FnZVGoRYxj5j6

ReplyDeleteLet 2p= perimeter of triangle ABC

Draw diameter KL of circle O (see sketch)

We have KL=MK+ML=2R….(1)

Note that M is the midpoint of TTa and TcTb ( see sketch)

In trapezoid EcEbTbTc we have MK=1/2(Rc+Rb)…(2)

In trapezoid ITEaTa we have ML=1/2(Ra-r)…. 3)

Combine (1), (2) and (3) we have 2R=1/2(Rc+Rb)+1/2(Ra-r)

And 4R+r= Ra+Rb+Rc

Draw NOMP perpendicular to BC (N,M on O). M midpoint of TcTb => MN middle line of trapez

ReplyDeleteMN = (Rc+Rb)/2 (1)

BTa=TC => MTa=MT. Draw NS perpnd to EaTa From congruece of tr

MP+r=Ra-MP (2)

From (1) and (2) Ra+Rb+Rc=4R+r