How do you prove that DCPQ is cyclic?

Question

900 views around the world

You can reuse this answer
Creative Commons License

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