Finding coordinates of rectangle on a curved surface

Question

Does anyone know how to calculate the coordinates of the rectangle/square box on the surface of the circle?

I can get the center of the rectangle and draw a line through it but trying to get the coordinates.

var lineHeight = 25;

var baseX = circle.x + circleRadius/2 * Math.cos(angleRadians);
var baseY = circle.y + circleRadius/2 * Math.sin(angleRadians);

var x1 = baseX + lineHeight*Math.cos(angleRadians);
var y1 = baseY + lineHeight*Math.sin(angleRadians);


this.testgraphics = this.add.graphics();
this.testgraphics.lineStyle(4, 0xff0000);
this.testgraphics.beginPath();
this.testgraphics.moveTo(baseX, baseY);
this.testgraphics.lineTo(x1, y1);
this.testgraphics.closePath();
this.testgraphics.strokePath();

Answer 1

Why do you use a half of circleRadius ( circleRadius/2 )?

baseX = circleCenterX + circleRadius * cos(angleRadians) 
baseY = circleCenterY + circleRadius * sin(angleRadians) 

corner coordinates

x1 = baseX - rectWidth / 2 * sin(angleRadians)   //note sign
y1 = baseY + rectWidth / 2 * cos(angleRadians) 

x2 = baseX - rectWidth / 2 * sin(angleRadians) + rectHeight * cos(angleRadians)  
y2 = baseY + rectWidth / 2 * cos(angleRadians) + rectHeight * sin(angleRadians) 

x3 = baseX + rectWidth / 2 * sin(angleRadians) + rectHeight * cos(angleRadians)  
y3 = baseY - rectWidth / 2 * cos(angleRadians) + rectHeight * sin(angleRadians)

x4 = baseX + rectWidth / 2 * sin(angleRadians) 
y4 = baseY - rectWidth / 2 * cos(angleRadians)