53
Prove that the tangents drawn to a circle at the end points of a diameter are parallel to each other.
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(b)
Let APB and CQD are tangents at the end points P and Q of diameter PQ of a circle with centre O.
$\angle APO = \angle DQO = 90^\circ$ (tangent is perpendicular to radius at the point of contact) (1 Mark)
$\angle APO$ and $\angle DQO$ are alternate interior angles (1 Mark)
$\therefore AB \parallel CD$ (1 Mark)
(b)
Let APB and CQD are tangents at the end points P and Q of diameter PQ of a circle with centre O.
$\angle APO = \angle DQO = 90^\circ$ (tangent is perpendicular to radius at the point of contact) (1 Mark)
$\angle APO$ and $\angle DQO$ are alternate interior angles (1 Mark)
$\therefore AB \parallel CD$ (1 Mark)