Given that , is a tangent, and
, find .
A tangent to a circle is perpendicular to the radius at its point of tangency.
is a tangent, so triangle is right-angled at .
The sum of the interior angles of a triangle is , so for triangle ,
We know that a straight line passing through the centre of a circle and the midpoint of any chord is perpendicular to the chord.
is the midpoint of , so
The sum of the interior angles of a quadrilateral is , so for the quadrilateral ,