$A$ circle $\odot(P, 5 \, cm)$ is given. Construct two tangents to the circle such that the measure of the angle between them is $60^\circ$. Write the steps of construction.
(N/A) $1$. Draw a circle with center $P$ and radius $5 \, cm$.
$2$. Draw a radius $PA$ and another radius $PB$ such that $\angle APB = 120^\circ$ (since the angle between tangents is $60^\circ$,the angle at the center is $180^\circ - 60^\circ = 120^\circ$).
$3$. At point $A$,construct a line perpendicular to $PA$.
$4$. At point $B$,construct a line perpendicular to $PB$.
$5$. Let these two perpendicular lines intersect at point $Q$. Then $QA$ and $QB$ are the required tangents,and $\angle AQB = 60^\circ$.
$2$. Draw a radius $PA$ and another radius $PB$ such that $\angle APB = 120^\circ$ (since the angle between tangents is $60^\circ$,the angle at the center is $180^\circ - 60^\circ = 120^\circ$).
$3$. At point $A$,construct a line perpendicular to $PA$.
$4$. At point $B$,construct a line perpendicular to $PB$.
$5$. Let these two perpendicular lines intersect at point $Q$. Then $QA$ and $QB$ are the required tangents,and $\angle AQB = 60^\circ$.
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