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WOLFRAM|DEMONSTRATIONS PROJECT

29. Construct a Triangle ABC Given the Length of AB, the Angle at C and the Sum of the Other Sides

​
c
1
a + b
1.45
γ
1.3
zoom
2
steps
1
2
3
4
5
second solution
ellipse
verification
This Demonstration shows how to construct a triangle
ABC
given the length
c
of side
AB
, the opposite angle
γ
at
C
and the sum of the lengths of the other two sides
a+b
.
Construction
1. Draw the segment
AB
of length
c
.
2. Draw the circle
τ
with center
S
so that
∠ASB=γ
.
3. Draw the circle
σ
with center
A
and radius
a+b
. The circles
τ
and
σ
meet at
D
and
D'
.
4. Let the point
C
be the intersection of the segment
AD
and the perpendicular bisector of
BD
.
5. Then
ABC
is the required triangle.
Verification
∠ADB=γ/2
since it is an arc corresponding to the central angle
∠ASB=γ
.
​
Since
BDC
is an isosceles triangle with apex
C
,
∠ACB=γ
and
BC=CD
.
Thus
AC+CB=AC+CD=a+b
.
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