Question

Statement:-Tangent at any point of a circle is perpendicular to the radius through the point of contact.

If yes enter $1$, else $0$

Answer 1

Construction Take point $B$ other than $A$ on the tangent $l$ Join $OB$, Let $OB$ meet the circle at point $C$.

Proof: We know that among all the line segment joining the point $O$ to a point on $l$, the perpendicular is the shortest to $l$

$OA=OC....$ (Radii of the same circle)

Now $OB=OC+BC$

$\Rightarrow OB>OC$

$\Rightarrow OB>OA$

$\Rightarrow OA<OB$

$B$ is an arbitary on the tangent $l$

Hence $OA$ is shorter than any other line segment joining $O$ to any point on $l$

Hence $OA\perp l$