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Indian Circle Problem

Source: IMO LongList 1988, India 5, Problem 40 of ILL

November 3, 2005

ratiogeometryrectanglegeometric transformationhomothetycircumcirclesymmetry

Problem Statement

i.) Consider a circle

K

with diameter

AB;

with circle

L

tangent to

AB

and to

K

and with a circle

M

tangent to circle

K,

circle

L

and

AB.

Calculate the ration of the area of circle

K

to the area of circle

M.

ii.) In triangle

ABC, AB = AC

and

\angle CAB = 80^{\circ}.

If points

D,E

and

F

lie on sides

BC, AC

and

AB,

respectively and

CE = CD

and

BF = BD,

then find the size of

\angle EDF.

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