Question

I really need some help in how to find or know the locus >.<

Given a fixed angle CAB. Find the locus of the points equidistant from the sides of 13 years ago

Answer 1

equidistant from two sides of an angle is the angle bisector
5 cm from a point is the circumference of the circle with center at point B with radius 5

the intersection of the circle and the angle bisector is the answer: 2 points

Answer 2

though if the circle is too small, no intersection, or possibly 1 tangent point....

Answer 3

How on earth do you find these things?! It's sooo confusing

Answer 4

You memorize (or learn) the various cases.

we can prove the angle bisector gives you the locus of points equidistant for both sides
(we use congruent right triangles)

It is (more or less) intuitive that the locus of points equidistant from a point is a circle (this is the definition of a circle)

Answer 5

And I don't think they want to know how many points.. =) I've memorized the cases or conditions. It's sometimes it's hard to find it =( But just one question on this, how did we know that point B is the center?

Answer 6

( mind the second "it's" :P )

Answer 7

distance of 5 cm from point B

the locus of all points 5 cm from B is a circle

The actual answer to this question could be

depends on how "big" 5 cm is. we need more info to know if the circle intersects the bisector line