MathDB

concurrency wanted, two circles related

Source: 2010 Balkan Shortlist G8 BMO

April 4, 2020

concurrentconcurrencyTangentscirclesgeometry

Problem Statement

Let

c(0, R)

be a circle with diameter

AB

and

C

a point, on it different than

A

and

B

such that

\angle AOC > 90^o

. On the radius

OC

we consider the point

K

and the circle

(c_1)

with center

K

and radius

KC = R_1

. We draw the tangents

AD

and

AE

from

A

to the circle

(c_1)

. Prove that the straight lines

AC, BK

and

DE

are concurrent

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