P and Q are points on sides AB and AD of square ABCD of side 1 unit such that perimeter of triangle PAQ is 2 units. Find angle PCQ

Question

square ABCD is of side 1 unit and perimeter of triangle PAQ is 2 units

Answer 1

square with each side = 1 unit

triangle formed with one vertex at a corner of the square

other 2 vertices are points on the adjoining sides

perimeter of the triangle is fixed = 2

what's the angle formed by another triangle with vertex at the opposite corner of the square and the other 2 vertices the same??

a rough WAG guess is 45 degrees = pi/4

as the perimeter gets larger, the angle approaches 90 degrees

as the perimeter gets smaller, the angle approaches 0 degrees

so with perimeter = 2, it's somewhere between 0 and 90, Go with the average = 45 degrees