Question

Quadrilateral ABCD is a parallelogram.
side BC intersects circle
at point P.
Prove that
DC=DP

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Answer 1

Answer: ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q.

Step-by-step explanation:

To prove: P, Q, C and D are concyclic. Construction: Join PQ. Extend side AP of the cyclic quadrilateral APQB to D. External angle, ∠1= interior opposite angle, ∠B Since, BA||CD and BC cuts them ∠B +∠C =180o Since, Sum of interior angles on the same side of the transversal = 180o Or ∠1+∠C =180o So, PDCQ is cyclic quadrilateral. Hence, the points P, Q, C and D are concyclic.