Given a triangle ABC that is right-angled at point A .The hypotenuse BC is fixed while A varies. Find the locus of point A.

Question

hartnn · Answer

any ideas ?

hartnn · Answer

after solving u get a CIRCLE

aroub · Answer

No, this one no idea at all!! Lol, I was about to say not circle.. Umm, how? They didn't say at a given distance or a given point, right?

hartnn · Answer

and we can use exactly the same diagram we used in last question

hartnn · Answer

here, just the condition is different

aroub · Answer

Yeah, but don't use it please!

hartnn · Answer

gues which theorem we gonna use when its given 'a right triangle' ?

hartnn · Answer

*guess

aroub · Answer

I always think of Pythagorean when it comes to right triangles

hartnn · Answer

that is absolutely correct!

aroub · Answer

But what does this theorem got to do with the locus?

hartnn · Answer

using pythagoras theorem and distance formula , we get the equation of locus in the form , $x^2+y^2=a^2$
which is the equation of circle.

aroub · Answer

please please don't use them here.. because they're more confusing! And I never took them. Do you have any other way? If not.. Just leave this question aside =)

hartnn · Answer

* 
$\~ \large (x-h)^2+(y-k)^2=a^2$

hartnn · Answer

question left ...

aroub · Answer

In the end it's circle right?

hartnn · Answer

absolutely!