Question

Show that tangent lines at the end points of a diameter of a circle are parallel.

Answer 1

Let $AB$ diameter of a given circle, and let $PQ$ and $RS$ be the tangents lines drawn to the circle at points $A$ and $B$ respectively.

Since tangent at a point to a circle is perpendicular to the radius through the point.

$AB\perp PQ$ and $AB\perp RS$

$\Rightarrow \angle PAB={90}^o$ and $\Rightarrow \angle ABS={90}^o$

$\Rightarrow \angle PAB=\angle ABS$

$\Rightarrow PQ\parallel RS$ [$\because \angle PAB$ and $\angle ABS$ are alternate angle]