What you’ll learn
Construct triangles from measurements.
Key idea
The two circles jointly enforce distances to A and B; the above-base condition selects one mirror intersection.
Circle centers/radii enforce specific labeled distances; mirror intersections require the specified above-base choice. No coordinate-distance algorithm required.
Worked example
Enter the exact value or ordered values in the format requested below.
Construct ABC with AB=9cm, AC=8cm, BC=3cm and C above AB. Create a labeled base-and-circle construction protocol; circle(center,radius) notation is used.
- Draw AB=9cm. Circle centered at A with radius 8 enforces AC=8; circle at B with radius 3 enforces BC=3.
- The side bounds 5<9<11 give two mirror intersections; choose the one above AB to obtain the required triangle.
Answer: AB=9; circle(A,8); circle(B,3); C=upper intersection
Quick Check
Choose which candidate representation satisfies the requirements of 'Construct triangles from measurements' and justify the choice.
For AB=8,AC=7,BC=6,C above AB, compare P:AB=8; circle(A,7); circle(B,6); C=upper intersection; Q:AB=8; circle(A,6); circle(B,7); C=upper intersection; R:AB=8,one circle at A radius7,any upper point. Select and justify all constraints.