# ABCD is a square. E is the midpoint of AB. Join EC and ED. EC intersects BD at N. Join AN intersecting BC at F. AN intersects ED at G. Prove DCFG is a cyclic quadrilateral? Any help is appreciated.

Grade:9

## 1 Answers

prince sunjot dutt
58 Points
3 years ago

In order to prove it is cyclic, we just need to prove the fact that sum of opposite angles of a cyclic quadrilateral is180•.i.e. $\dpi{50} \zeta \angle$DGF+$\dpi{50} \zeta \angle$DCF=180•. Simce , it is already given that $\dpi{50} \zeta \angle$DCF=90. So, just prove that​ $\dpi{50} \zeta \angle$DGF=90.