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P is on the locus of points equidiatant from two given points X and Y….

P is on the locus of points equidiatant from two given points X and Y. UV is a straight line throuh Y parallel to the locus. If < PYU is 40°, find < XPY.

A.
100^o
B.
80 ^o
C.
50 ^o
D.
40 ^o

Correct Answer: Option B

Explanation

< PYU = < YPQ = 40°(Alternative) = PQ(parallel)UV
< XPQ = < YPQ = 40°, Since QX = QY
therefore < XPY = 80°