IMO 1988 LL INA45

(a) Consider a circle K with diameter AB, a circle L tangent to AB and

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IMO 1988 LL INA45

Origin: INA

Problem

(a) Consider a circle K with diameter AB, a circle L tangent to AB and to K, and a circle M tangent to circle K, circle L, and AB. Calculate the ratio of the area of circle K to the area of circle M. (b) In triangle ABC, AB = AC and ∡CAB = 80◦. If points D, E, and F lie on sides BC, AC, and AB, respectively, and CE = CD and BF = BD, find the measure of ∡EDF.