Geometric Bites

Below I demonstrate how to find the line that passes through two intersecting circles. Part 1 Part 2 Part 3   There is a free interactive graph that shows why this is correct. https://www.desmos.com/calculator/z9rh2ri9bz

Below is an example of how to find the region where two circles on a 2 dimensional plane overlap . The workings are in high resolution... To demonstrate the workings are indeed correct, a free graph has been created on Desmos: https://www.desmos.com/calculator/0aonrev54r

In this post I demonstrate how to find out where a line and circle intersect on a 2 dimensional plane. The first step is to write out the equations of a line and a circle. We then make sure for both equations 'y' is isolated . Once we have the equations for a line and a circle whereby 'y' is isolated, we can then go about finding the values of 'x' for where the line intersects the circle. Like so... After we have found the values of 'x' using the quadratic formula , we then plug them back in to y=mx+c to get the values of 'y' for which the line intersects the circle. And that's it basically. Below is a free interactive Desmos graph related to this work: https://www.desmos.com/calculator/w3tsnjajtx