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    \tikzstyle{help lines}+=[very thin]

    \coordinate[label={[label distance=0.5em]180:$A$}]
        (A) at (120:5);
    \coordinate[label={[label distance=0.5em]180:$B$}]
        (B) at (210:5);
    \coordinate[label={[label distance=0.5em]  0:$C$}]
        (C) at (335:5);
    \coordinate[label={[label distance=0.5em]  0:$D$}]
        (D) at ( 40:5);
    \coordinate[label={[label distance=0.5em]-90:$M$}]
        (M) at (intersection of A--C and B--D);

    \draw (A) -- (B) -- (C) -- (D) -- (A);
    \draw (A) -- (C) (B) -- (D);

In the example above, how to construct a point E on AC so that ∠ADE = ∠BDC?

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up vote 6 down vote accepted

This looks like a job for the excellent tkz-euclide package. The syntax takes a bit of getting used to, but it's very powerful:



% Define the known points

% Find the intersection between AC and BD, save point as M

% Measure the angle BDC, save as \angleBDC

% Rotate A by \angleBDC around D, save point as E'
\tkzDefPointBy[rotation=center D angle \angleBDC](A)

%Find the intersection between AC and DE', save point as E



\tkzLabelPoints[below left](E)
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Is there a way to use \tkzLabelAngle[pos = 0.8](B,A,C){angleBAC} for writing that value near the angle? – Arne Timperman Aug 24 '13 at 17:52
\tkzGetAngle{angleBAC}; \tkzLabelAngle[pos = 0.8](B,A,C){\tkzAngleResult}; – Arne Timperman Aug 24 '13 at 18:20

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