Question

AP is perpendicular to CD and CQ is perpendicular to AD.prove that quadrilateral ACPQ is cyclic

Answer 1

I tried to solve it via diagram itself
here ∆AQP and ∆CQP are congruent AAA property

with that we can get all angles as same
now with Vertically opposite angle we get angles AOC as 120 deg
now ∆ POQ and ∆AOC are also very similar where in angles PAC and angles QCA are same. that makes the angles as 30 deg [ (180 - 120) / 2 ]

now if you see the opposite angles of quad ACPQ are supplementary
hence it's cyclic quadrilateral

let me know if you still don't get it.

thanks