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 4 of 5: Locate the possible vertex

B

Previous step Next step

B\in a,\qquad CB=A'C\quad(a\parallel p\text{ through }A)

Detailed analysis

Let $a$ be the line through $A$ parallel to $p$ . Since $B\in P$ , it must lie on $a$ . Draw the circle centered at $C$ with radius $A'C$ . Its intersections with $a$ are exactly the possible $B$ , because the common leg condition is $BC=A'C$ .