How to draw this?

Question

The measure of a line segment PC, perpendicular to hypotenuse AC of right triangle ABC, is equal to the measure of leg BC. Show BP may be perpendicular or parallel to the bisector of angle A

Answer 1

This is difficult to describe, but I'll try.  Draw a right triangle and label the corners A, B, C, with B being the right angle.  Now draw a line through point C that is perpendicular to AC and is twice the length of BC, and whose midpoint is C.  Label the two ends of this line segment P.  Draw a line from each P to B.  Draw a line that bisects angle A.  This line will be perpendicular to one BP line segment, and parallel to the other BP line segment.

 

I hope this helps.