and
are points on a semicircle. The tangent at
meets the extended diameter of the semicircle at
, and the tangent at
meets it at
, so that
and
are on opposite sides of the center. The lines
and
meet at
.
is the foot of the perpendicular from
to
. Show that
bisects angle
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$C$ and $D$ are points on a semicircle. The tangent at $C$ meets the extended diameter of the semicircle at $B$, and the tangent at $D$ meets it at $A$, so that $A$ and $B$ are on opposite sides of the center. The lines $AC$ and $BD$ meet at $E$. $F$ is the foot of the perpendicular from $E$ to $AB$. Show that $EF$ bisects angle $CFD$
Školjka