In the diagram below, OP is circumscribed about quadrilateral ABCD. What is the value of X

place r′ so that qr′ is parallel to the tangent.

now we get that ∠r′py=∠pr′q, where y is on the tangent, on the opposite side of p from x.

also, because of the symmetry, ∠r′py=∠qpx.

finally, note that no matter where we place r, as long as it's on the correct arc, we have ∠prq=∠pr′q.

stringing all these equalities together, we end up with ∠prq=∠qpx.

this picture will show how its going to look like.

hope this by jack monhen

a reflection across line m

step-by-step explanation:

the first transformation is a 90 degree rotation counterclockwise around the point g. this gets to image gh'j'k'. when the image gh'j'k' is reflected over the line  m the result is g'h"j"k". the final transformation is a reflection over the line  m.