Circle in three geo-coordinates?

Question

PHP

There are coordinates of three points on the map.
It is necessary to find the coordinates of the center of the circle circumscribed around the resulting triangle.
The classical geometric solution through perpendiculars does not fit, without a polynomial transformation, I really don’t want to perform the latter (and, to be honest, it’s not entirely clear how to do it).
Any ideas how to find the center in an easier way?
the calculation is carried out on php

here is a specific example. The required three points are indicated in the form of crosses, the fourth cross is the center of the circle, obtained using the classical approach from geometry, through perpendiculars
the problem as a whole (from real estate topics):
Yandex maps cannot determine street intersections (
We came up with this method: there is a base with houses (located on the streets) and the coordinates of these houses. It is necessary to find the intersection of two obviously intersecting streets.
We select all the houses along these streets and look for houses that are, for example, within 200 meters from each other (but on different streets of the EU, i.e. we compare each house from one street with each house on another street). In fact, this is exactly what is shown in the picture (different streets = different icons). Next, it is already necessary to determine the approximate area in which the house will be located, indicated in the ad as "the intersection of Tukhachevsky and Magnitogorskaya streets." Approximate area = circle

Answer 1

Using the coordinate method. For example, for 1 and 2 points, build the equation of a straight line equidistant from these two points. Then the same thing, for example, for 2 and 3 points. The intersection of these two lines will be the center of the circle. Radius - obviously, the distance from the center to any of the points.

Answer 2

Once again... Do I understand correctly... Do you need a circle that passes through 3 given points (which uniquely define a circle)?

Answer 3

Please explain whether you need a circle that passes through all three points, or do you need a circle that contains all three points inside?

Answer 4

A classic Olympiad programming problem, solutions can be found here .

Answer 5

I'm afraid without painstaking work with spherical coordinates nothing good will come of it. But drawing such a “circle” will not be easy.
If the radius is small, as you have in the figure, then it should be considered through perpendiculars. Check the entries again.

Answer 6

puffed up ... I'm sorry ...
What I said is true for acute-angled ones (each angle < 90), otherwise what havk said
> If there are 3 points, and you need a circle inside which all three points will be, then its center will be a point that is the middle of the the long side of the triangle that these points form.
If 1x != 1y - convert to a normal Cartesian coordinate system and do what we described.