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A is a give point and P is any point on a given straight line. If AQ=AP and AQ makes a constant angle with AP find the locus of Q.

I think the answer is that the locus would be a circle or a sector of circle

Just wanna confirm it. Thanks in advance

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No, this will not be a circle.

Your operation rotates $P$ around $A$ by a fixed angle. What happens to a line when you rotate it?

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  • $\begingroup$ A sector I guess and in the question also I wrote a circle or a sector $\endgroup$ – Apoorv Jain May 30 '14 at 13:09
  • $\begingroup$ First of all, the line does not have to pass through $A$, does it? But more importantly, you seem to be thinking of the area that is swept by the line, but you want to know where the line goes after the rotation, not where it passes through. $\endgroup$ – Tara May 30 '14 at 13:18
  • $\begingroup$ @user3650050 It will be a circle if the distance $AP$ is fixed and you change the angle. In your case, the angle is fixed while the distance $AP$ is changing. $\endgroup$ – achille hui May 30 '14 at 13:19
  • $\begingroup$ Got it you my fault oh damn the answer will be arc???? $\endgroup$ – Apoorv Jain May 30 '14 at 13:26
  • $\begingroup$ @user3650050 If you take a pencil and rotate it 30 degrees, does it become an arc? $\endgroup$ – Tara May 30 '14 at 15:58
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A is the fixed center of a rigid lamina sector PAQ entirely rotating about vertex point A inside a full circle whose radius AP=AQ. Arc PQ, point P or point Q follows or traces circumference of this full circle.

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