$A$ circle $\odot(P, 4)$ is given. Draw a pair of tangents such that the measure of the angle between the tangents at their point of intersection $A$ is $60^\circ$.
(N/A) Data: Draw $\odot(P, 4 \text{ cm})$.
To construct: Draw a pair of tangents to $\odot(P, 4 \text{ cm})$ such that the measure of the angle between the tangents at their point of intersection $A$ is $60^\circ$.
$(1)$ Draw $\odot(P, 4 \text{ cm})$ and two radii $\overline{PR}$ and $\overline{PQ}$ such that $m\angle RPQ = 180^\circ - 60^\circ = 120^\circ$.
$(2)$ Through $R$,draw a line perpendicular to $\overline{PR}$.
$(3)$ Through $Q$,draw a line perpendicular to $\overline{PQ}$.
$(4)$ Let the lines drawn in step $(2)$ and step $(3)$ intersect at $A$.
Thus,$\overleftrightarrow{AR}$ and $\overleftrightarrow{AQ}$ are the required tangents such that the measure of the angle between them is $60^\circ$.
To construct: Draw a pair of tangents to $\odot(P, 4 \text{ cm})$ such that the measure of the angle between the tangents at their point of intersection $A$ is $60^\circ$.
$(1)$ Draw $\odot(P, 4 \text{ cm})$ and two radii $\overline{PR}$ and $\overline{PQ}$ such that $m\angle RPQ = 180^\circ - 60^\circ = 120^\circ$.
$(2)$ Through $R$,draw a line perpendicular to $\overline{PR}$.
$(3)$ Through $Q$,draw a line perpendicular to $\overline{PQ}$.
$(4)$ Let the lines drawn in step $(2)$ and step $(3)$ intersect at $A$.
Thus,$\overleftrightarrow{AR}$ and $\overleftrightarrow{AQ}$ are the required tangents such that the measure of the angle between them is $60^\circ$.
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