Problem 6

Two planes

P

and

Q

intersect along line

p

. Points

A\in P

and

C\in Q

are not on

p

. Construct an isosceles trapezoid

ABCD

with

AB\parallel DC

, an incircle, and vertices

B\in P

D\in Q

Step 3 of 5: Construct the required average length

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AA'\perp DC,\qquad A'C=\frac{AB+DC}{2}

Detailed analysis

Through $A$ draw the perpendicular $AA'$ to the line $DC$ (parallel to $p$ ), with $A'\in DC$ . The right-angled rectangle formed by the two parallel base lines shows that $A'C$ is the average of the two base lengths, and hence equals the common leg length.