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If perpendiculars from any point within an angle on its arms are equal prove that it lies on the bisector of that angle.

Mathematics
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I don't know what "on its arms" means. maybe the drawing above illustrates this.
yep..your figure seems correct and the angle bisector thing can be proved by congruence straightaway..

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Other answers:

I'm sorry, went offline for a while.
@shubhamsrg I know it should be done by congruence but I don't know how ....
Please help ....
RHS,,you see that?
I AM AN IDIOT. Yeah I didn't think of that. thanks for your help!!!
glad to help.. ^_^

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