MathDB

Two half-lines

a

and

b

, with the common endpoint

O

, make an acute angle

\alpha

. Let

A

a

and

B

b

be points such that

OA=OB

, and let

b

be the line through

A

parallel to

b

. Let

\beta

be the circle with centre

B

and radius

BO

. We construct a sequence of half-lines

c_1,c_2,c_3,\ldots

, all lying inside the angle

\alpha

, in the following manner: (i)

c_i

is given arbitrarily; (ii) for every natural number

k

, the circle

\beta

intercepts on

c_k

a segment that is of the same length as the segment cut on

b'

a

and

c_{k+1}

. Prove that the angle determined by the lines

c_k

and

b

has a limit as

k

tends to infinity and find that limit.

Problem Statement