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P and Q are fixed points, and X is a variable point which moves so...

Mathematics
JAMB 1980

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
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Correct Answer: Option C
Explanation

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.


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Post-UTME Past Questions - Original materials are available here - Download PDF for your school of choice + 1 year SMS alerts
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Post-UTME Past Questions - Original materials are available here - Download PDF for your school of choice + 1 year SMS alerts
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