29. Construct a Triangle ABC Given the Length of AB, the Angle at C and the Sum of the Other Sides
29. Construct a Triangle ABC Given the Length of AB, the Angle at C and the Sum of the Other Sides
This Demonstration shows how to construct a triangle given the length of side , the opposite angle at and the sum of the lengths of the other two sides .
ABC
c
AB
γ
C
a+b
Construction
1. Draw the segment of length .
AB
c
2. Draw the circle with center so that .
τ
S
∠ASB=γ
3. Draw the circle with center and radius . The circles and meet at and .
σ
A
a+b
τ
σ
D
D'
4. Let the point be the intersection of the segment and the perpendicular bisector of .
C
AD
BD
5. Then is the required triangle.
ABC
Verification
∠ADB=γ/2
∠ASB=γ
BDC
C
∠ACB=γ
BC=CD
Thus .
AC+CB=AC+CD=a+b