Question

Determine the angle between the lines passing through the center and bisecting the chords AC and CB.
degrees

Answer 1

In the given figure, AB is the diameter.
Hence it will subtend ${90}^o$ at C.

The line that bisects any chord and passes through the center is perpendicular to the chord.

Hence, OD and OE are perpendicular to AC and CB, respectively.

Sum of the interior angles of the quadrilateral is ${360}^o.$
$\Rightarrow \angle ODC+\angle DCE+\angle CED+\angle DOE={360}^o$
$\Rightarrow \angle DOE={360}^o-3\times {90}^o={90}^o$

$\therefore$ The required angle is ${90}^o.$