## aroub 3 years ago 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.

1. hartnn

any ideas ?

2. hartnn

after solving u get a CIRCLE

3. aroub

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?

4. hartnn

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

5. hartnn

here, just the condition is different

6. aroub

Yeah, but don't use it please!

7. hartnn

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

8. hartnn

*guess

9. aroub

I always think of Pythagorean when it comes to right triangles

10. hartnn

that is absolutely correct!

11. aroub

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

12. hartnn

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.

13. aroub

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 =)

14. hartnn

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

15. hartnn

question left ...

16. aroub

In the end it's circle right?

17. hartnn

absolutely!