# Find a point that best fits criteria

kevvvli123 shared this question 1 year ago

For example, if I have a circle with diameter AB and I want a point P such that AP/BP = 2.

I know this particular example could be done with some geometric properties, but I want a generalized way to do this. Like find a point on a parabola such that the ratio of distance from circle w_1 and w_2 is 11/3 or something.

I just want GeoGebra to test like a million points and find the best one. Is there a way to do this? 1

```a point P such that AP/BP = 2
```

I think there are infinite such points. Do you want them all? (ie a locus) 1

Or do you mean it has to lie on the circle? 1 1

AP= ratio*BP is a circle. create it and intersect with the object you want

for another objects think that ie: distance(P,circle)=distance(P,centre)-radius etc

share news construction if you need help

Files: foro.ggb 1

sorry

type eq1: (x - x(A))² + (y - y(A))² = ratio^2 * ((x - x(B))² + (y - y(B))²) in foro.ggb attached in previous post for better use of ratio

¡marditas prisas! 1

This is actually Apollonius circle construction controlled (by slider-ratio)..GIven segment AB, divide it internally and externally at points C and D using the ratio value and then draw circle with CD as the diameter. Any point P on this circle divides AB in the given ratio. 1

.....(continued)... Intersection points with another given curve with Apollonius circle will be the required points in general.  1

Yo propuse este método porque se puede adaptar a otras situaciones

por ejemplo a una circunferencia y una recta

Files: foro.ggb 1

Thank you Sir, for taking note of me - a novice on this GeoGebra platform. I always keenly study your intelligent solutions. 