MathDB

Unit square

ABCD

is divided into four rectangles by

EF

and

GH

, with

BF = \frac14

EF

is parallel to

AB

and

GH

parallel to

BC

EF

and

GH

meet at point

P

. Suppose

BF + DH = FH

, calculate the nearest integer to the degree of

\angle FAH

. [asy] size(100); defaultpen(linewidth(0.7)+fontsize(10)); pair D2(pair P) { dot(P,linewidth(3)); return P; } // NOTE: I've tampered with the angles to make the diagram not-to-scale. The correct numbers should be 72 instead of 76, and 45 instead of 55. pair A=(0,1), B=(0,0), C=(1,0), D=(1,1), F=intersectionpoints(A--A+2*dir(-76),B--C)[0], H=intersectionpoints(A--A+2*dir(-76+55),D--C)[0], E=F+(0,1), G=H-(1,0), P=intersectionpoints(E--F,G--H)[0]; draw(A--B--C--D--cycle); draw(F--A--H); draw(E--F); draw(G--H); label("

A

",D2(A),NW); label("

B

",D2(B),SW); label("

C

",D2(C),SE); label("

D

",D2(D),NE); label("

E

",D2(E),plain.N); label("

F

",D2(F),S); label("

G

",D2(G),W); label("

H

",D2(H),plain.E); label("

P

",D2(P),SE); [/asy]

Problem Statement