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WOLFRAM|DEMONSTRATIONS PROJECT

6. Construct a Triangle Given Its Circumradius, Inradius and the Length of Its Base

0.7

0.3

step 1

step 2

step 3

show incircle

This Demonstration constructs a triangle

ABC

given the circumradius

, inradius

and the length of the base

AB=c

Construction

Draw a circle

of radius

and a chord

of length

Step 1: Let

be the midpoint of

and let the right bisector of

meet

at the point

Step 2: Draw a second circle

with center

through

and

. Draw a (green) line

perpendicular to

so that

DF=r

. Clearly

is parallel to

Step 3: Let

be one of the points of intersection of

and

. The point

is the intersection of

and the ray

Verification

Let

∠CAB=α

∠ABC=β

and

∠BCA=γ

Since arc

equals arc

bisects

∠ACB

and

∠BAE=γ/2

. Also

∠AEG=∠ABC=β

. The triangle

AEG

is isosceles, so

∠EAG=π/2-β/2

. Then

∠GAB=∠GAE-∠BAE=π/2-β/2-γ/2=α/2

. So

is the incenter of

ABC

with distance

from

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