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 1 of 5: Choose the direction of the bases

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In plain words

Each base lies in one of the two planes, and the two planes meet only along $p$ .

AB\parallel DC\parallel p

Detailed analysis

The lines $AB$ and $DC$ are coplanar with $p$ in their respective planes. If one were not parallel to $p$ , both would meet $p$ , forcing the two base lines to be skew rather than parallel. Hence the required parallel bases must both be parallel to $p$ .