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Finding angle values such that quadrilateral is tangent

Source: Turkey IMO TST 1993 #5

July 7, 2011

geometrytrigonometrygeometry unsolved

Problem Statement

Points

E

and

C

are chosen on a semicircle with diameter

AB

and center

O

such that

OE \perp AB

and the intersection point

D

AC

and

OE

is inside the semicircle. Find all values of

\angle{CAB}

for which the quadrilateral

OBCD

is tangent.