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consider triangle OPY and OQZ
OY=OZ
angle OPY=OQZ =90°
OP=OQ
therefore triangles OPY and OQZ are congruent
as a result we can say PY=QZ (1)
consider triangle PXO and QXO
XO common side
angle XQO=XPO=90°
OP=OQ
triangles PXO and QXO are congruent
as a result we can say PX=QX (2)
from 1 and 2 we can write PY+PX=QZ+QX=> XY=XZ implies XYZ is an isoceles triangle
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