I have a circle with a line that is drawn through it at two points. I have the coordinate for the ce

kramberol

kramberol

Answered question

2022-07-14

I have a circle with a line that is drawn through it at two points. I have the coordinate for the center of the circle, the two coordinates where it intersects the circle and the radius as well. I want to put the two rectangles around the two pieces from the circle. My question is how can I get the coordinates of the rectangle?

Answer & Explanation

furniranizq

furniranizq

Beginner2022-07-15Added 20 answers

Step 1
Assuming the center to be the origin, compute r A + B 2 . This is the amount of offset needed. The direction is given by A + B 2 , so the complete formula is
O = r A + B 2 A + B 2 A + B 2 = 2 r A + B 2 A + B ( A + B )
bandikizaui

bandikizaui

Beginner2022-07-16Added 7 answers

Step 1
Find the angular coefficient of the line between the points A and B
( m = A y B y A x B x )
and q (where the line crosses the y-axis), and solve the system of the equation of the circle and the line, letting Δ = 0 . Let ( C x , C y ) be the centre of the circle, and r its radius.
{ ( x C x ) 2 + ( y C y ) 2 = r 2 y = m x + q
Let Δ = 0 , because if Δ > 0 there are 2 solutions there are 2 common points between the line and the circle, otherwise Δ < 0 there are no intersections.

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