Question

Given a triangle ABC such that B and C are fixed. Point A varies such that segment AB is congruent to segment AC. Find the locus of A.

Umm, an angle bisector maybe?

Answer 1

perpendicular bisector of BC

Answer 2

Aoh -.- I get it now! Because they said that the sides are congruent so they are equidistant so it's perpendicular bisector!! Let me draw it and tell me if it's right or wrong, okay? :)

Answer 3

sure

Answer 4

Sure. You are welcome.

Answer 5

do u know how to solve this algebraically ?

Answer 6

how to get to 'perpendicular bisector of BC'

Answer 7

Emmm, i don't think so.. like what do you mean? show me? :)

Answer 8

Does it matter?

Answer 9

Yea..the point A can be above BC or below BC according to that figure

Answer 10

Okay, thank youu!

Answer 11

ok, i choose point B as origin of my co-ordinate axes and point C on x-axis.
as they are fixed i can put them wherever i want.
now let co-ordinates of A be (x,y)
we need a locus in terms of x and y
let me draw it.

now AB=AC
will give you, using distance formula,
\(\huge x^2+y^2=(x-a)^2+y^2\)
can u simplify this and tell me what u get ?