MathDB

BE = BF wanted, tangents to a circle (O)

Source: Indonesia INAMO Shortlist 2017 G5 https://artofproblemsolving.com/community/c1101409_indonesia_shortlist__geometry

November 15, 2021

geometryequal segments

Problem Statement

Given a circle

(O)

with center

O

and

P

a point outside

(O)

A

and

B

are points on

(O)

such that

PA

and

PB

are tangents to

(O)

. The line

\ell

through

P

intersects

(O)

at points

C

and

D

, respectively (

C

lies between

P

and

D

). Line

BF

is parallel to line

PA

and intersects line

AC

and line

AD

E

and

F

, respectively. Prove that

BE = BF