How do you prove that DCPQ is cyclic?

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Answer 1 · 2017-11-11T05:30:13

The quadrilateral $ABCD$ is cyclic

So $/_ADC+/_ABC=180^@......[1]$

Again $/_ADC+/_QDC="sraight"/_ADQ=180^@......[2]$

Combining [1] and [2] we get

$/_ABC=/_QDC......[3]$

Now $QP"||"AB$ and $PB$ is the intercept

Hence $/_QPC+/_ABC=180^@.....[4]$

Combining [3] and [4]

#/_QPC+/_QDC=180^@

These are opposite angles of the quadrilateral $DCPQ$

Hence this is cyclic quadrilateral