Circles through different points
Refer to the adjacent animation.
- You can draw infinite number of circles passing through a given point 'P'.
- Again, there is no limit to the number of circles that can be drawn through two given points P and Q.
- You cannot draw a circle passing through 3 points on a line (i.e., collinear).
Consider three collinear points P, Q and R.
You can only draw a circle passing through any two points on the line, with the third lying inside or outside the circle.
- On the other hand, if the three points (P, Q and R) are non-collinear, then you can draw one and only one circle passing through them, i.e., the circle passing through 3 given non-collinear points is unique.
The points P, Q & R form a triangle PQR. The above circle passing through the 3 vertices ΔPQR is called as the circumcircle. 'O' is called the circumcenter. OP or OQ or OR is the circumradius.