P and Q are fixed points, and X is a variable point which moves so that angle PXQ = 45º. What is the locus of x?
A
A pair of straight lines parallel to PQ
B
The perpendicular bisector of PQ
C
An arc of a circle passing through P and Q
D
A circle with diameter PQ
E
The bisector of angle PXQ
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Constant Angle Rule:
In geometry, the locus of points from which a line segment subtends a constant angle is an arc of a circle.
Inscribed Angle Theorem:
This theorem states that angles subtended by the same arc at the circumference of a circle are equal. Consequently, as the point moves along the arc, the subtended angle remains constant.
Source: Myschool Past Questions Archive (Record #32616)