Thales Inscribed Angle Theorem Demonstrated Using JSXGraph

Thales inscribed angle theorem states the angle at \(P'\) below is smaller than that at \(P\) if \(P\) is inside the circle, and larger if it is outside the circle. Furthermore, for a fixed segment \(AB\) inside the circle, the angle at \(P'\) will always be the same regardless of where on the circle \(P'\) is, as long as it is on the same side of \(AB.\)

Try moving the points \(P,\) \(A\) or \(B\) around to see how it affects the angles!

Source Code

window.onload = function() {
    var M = 6;
    brd = JXG.JSXGraph.initBoard('box',{
        boundingbox:[-M,M,M,-M],
        grid: false,
        showCopyright:false,
        showNavigation:false
    });

    o = brd.create('point', [0, 0], {name: 'O'});
    c = brd.create('circle', [o, 4], {name: 'C'});

    a = brd.create('glider', [3, 0, c], {name: 'A'});
    b = brd.create('glider', [-3, -3, c], {name: 'B', label:{offset:[-15,0]}});
    p = brd.create('point', [-1, 2], {name: 'P'});

    opts = {strokeColor: 'blue'};
    lab = brd.create('segment', [a, b], opts);

    opts = {strokeColor: 'blue'};
    lpb = brd.create('segment', [p, b], opts);
    lpa = brd.create('segment', [a, p], opts);

    op = brd.create('line', [o, p], {visible: false});

    pp = brd.create('intersection', [c, op, 0], {name: 'P\'', label:{offset:[0,15]}});
    opts = {strokeColor: 'green'};
    lppb = brd.create('segment', [pp, b], opts );
    lppa = brd.create('segment', [a, pp], opts);
    opts = {strokeColor: 'lightblue', strokeWidth: '1px'};
    lopp = brd.create('segment', [o, pp], opts);

    angp = brd.create('angle', [b, p, a]);
    angpp = brd.create('angle', [b, pp, a]);

    var setAngleLabels = function() {
        angp.setLabelText(angp.Value().toFixed(2));
        angpp.setLabelText(angpp.Value().toFixed(2));
    };

    setAngleLabels();
    brd.addHook(function() { setAngleLabels(); }, 'move');
};

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