## aroub 3 years ago 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 <CAB that are at a distance of 5 cm from point B.

1. phi

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

2. phi

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

3. aroub

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

4. phi

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)

5. aroub

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?

6. aroub

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

7. phi

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 |dw:1352048840615:dw| depends on how "big" 5 cm is. we need more info to know if the circle intersects the bisector line

8. aroub

Well, it's not construction so it doesn't matter right now. But I will go with the first one.

9. aroub

I'm posting another few questions.. If you would please help me =) Because you and Hero are like the most people that I know are VERY good in geometry.