## Friday, December 25, 2009

### Problem 408: Cyclic quadrilateral, Perpendicular, Parallelogram, Congruence

Proposed Problem
Click the figure below to see the complete problem 408 about Cyclic quadrilateral, Perpendicular, Parallelogram, Congruence.

Complete Problem 408
Level: High School, SAT Prep, College geometry

1. extend BF to P, and CG to Q ( P and Q on circle )

a) ang NBC = ang FPQ ( BP//CQ, and BPQC cyclic) (1)

b) join A to Q, ang ADE = ang AQG ( have same arc ABC)
=> ang EAG = ang GAQ
=> GQ = GM (2)

c) at the same way
=> NF = FP (3)

d) from (2) and (3)
ang MNF = ang FPQ (4)

e) from (1) and (4)
ang NBC = ang FNM
=> BC//NM

2. can you tell me, please
why my solution is deleted

3. Accidentally deleted.

Following the solution posted by c.t.e.o on December 27, 2009.

extend BF to P, and CG to Q ( P and Q on circle )

a) ang NBC = ang FPQ ( BP//CQ, and BPQC cyclic) (1)

b) join A to Q, ang ADE = ang AQG ( have same arc ABC)
=> ang EAG = ang GAQ
=> GQ = GM (2)

c) at the same way
=> NF = FP (3)

d) from (2) and (3)
ang MNF = ang FPQ (4)

e) from (1) and (4)
ang NBC = ang FNM
=> BC//NM

4. thanks

the main idea of solution was