Colinear points

[tawdry sparrow]

How do I prove that 3 points are colinear?

[dusky granite]

One way is to check the slopes of the line segments connecting the points, if the slope AB equals the slope of BC then the points are colinear

@tawdry sparrow

[serene nimbus]

or just prove that they lie in the same line

[willow juniper]

There is a plenty of methods to do this, for example:
1.Menelai theorem;
2.Proof that 3 points lie on radical axis of two circles(have same power of point above two of them);
3. Proof that vectors are collinear;
4.Brianshon Theorem;
5.Pascal Theorem;
6.Just proof that angels are equal;
7.Simson line;
8.3 points lie on one circle after inversion with it center;
9.Homothety and composition of 3 homothety;
And more….

[long nova]

Just find the area of the triangle formed by these points

If it's 0

They're collinear

[tawdry sparrow]

thanks guys

[rugged lotus]

.solved