22

Part of 2021 BMT

Problems(2)

BMT 2021 Guts Round p22

Source:

\vartriangle ABC

D

E

be points on the angle bisector of

\angle BAC

\angle ABD = \angle ACE =90^o

. Furthermore, let

F

be the intersection of

AE

BC

O

be the circumcenter of

\vartriangle AF C

\frac{AB}{AC} =\frac{3}{4}

AE = 40

BD

EF

, compute the perpendicular distance from

A

OF

BMT 2021 General p22

Source:

Austin is at the Lincoln Airport. He wants to take

5

successive flights whose destinations are randomly chosen among Indianapolis, Jackson, Kansas City, Lincoln, and Milwaukee. The origin and destination of each flight may not be the same city, but Austin must arrive back at Lincoln on the last of his flights. Compute the probability that the cities Austin arrives at are all distinct.