$\odot(P, 4\, cm)$ is given. Construct two tangents to the circle which are perpendicular to each other. Write the steps of construction.
(N/A) $1$. Draw a circle with center $P$ and radius $4\, cm$.
$2$. Draw two perpendicular diameters $AB$ and $CD$ of the circle,intersecting at the center $P$.
$3$. At points $A, B, C,$ and $D$,draw tangents to the circle using a set square or by constructing $90^{\circ}$ angles at each point.
$4$. Let the tangents at $A$ and $C$ intersect at point $Q$. Since the radii $PA$ and $PC$ are perpendicular,the quadrilateral $PAQC$ is a square (as all angles are $90^{\circ}$ and adjacent sides are equal to the radius).
$5$. Thus,the tangents at $A$ and $C$ are perpendicular to each other at point $Q$.
$2$. Draw two perpendicular diameters $AB$ and $CD$ of the circle,intersecting at the center $P$.
$3$. At points $A, B, C,$ and $D$,draw tangents to the circle using a set square or by constructing $90^{\circ}$ angles at each point.
$4$. Let the tangents at $A$ and $C$ intersect at point $Q$. Since the radii $PA$ and $PC$ are perpendicular,the quadrilateral $PAQC$ is a square (as all angles are $90^{\circ}$ and adjacent sides are equal to the radius).
$5$. Thus,the tangents at $A$ and $C$ are perpendicular to each other at point $Q$.
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