Try dragging point P and notice that angles stay constant. Notice that by construction ⟨(P,t1,O) & ⟨(P,t0,O) are orthogonal. We could have used dg.Tangent(Point, Circle) function built in dg.js

dg.js example code

		var canvas = dg.Canvas("testcanvas", { border: "1px solid #ccc"});
		var axes = dg.Axes([canvas.width() / 4, canvas.height() / 1.5]).hide(false);
		
		var p1 = dg.Point([1, 1]).label("O");
		var p2 = dg.Point([4, 2]).label("B");		
		var c0 = dg.Circle(p1,p2);
		var p3 = dg.Point([8, 3]).label("P");
		
		var midpoint = dg.Midpoint(p1, p3).label("M");
		var c1 = dg.Circle(midpoint, p3);
		dg.Line(p3, p1);
		
		var intersections = dg.Intersect(c0, c1);
		
		intersections[0].label("t0");
		intersections[1].label("t1");
		
		dg.Line(p3, intersections[0]);
		dg.Line(p3, intersections[1]);
		
		dg.Angle(p3, intersections[0], p1);