Construct a circle of radius 5 cm . Then construct a pair of tangents to the circle such that the angle between them is \( 60^{\circ} \).

To construct a pair of tangents to a circle such that the angle between them is \( 60^{\circ} \), follow these steps: ### Step 1: Draw the Circle 1. **Draw a circle** with a radius of 5 cm. Label the center of the circle as point \( O \). ### Step 2: Draw the Radius 2. **Draw a radius** \( OA \) of the circle, where \( A \) is a point on the circumference of the circle. ### Step 3: Construct the Angle 3. **Construct an angle of \( 60^{\circ} \)** at point \( O \): - Use a protractor to measure \( 60^{\circ} \) from the radius \( OA \) and mark point \( B \) on the circle. ### Step 4: Draw the Tangents 4. **Draw the tangents**: - From point \( A \), draw a line that is tangent to the circle. This line will touch the circle at point \( A \) and will be perpendicular to the radius \( OA \). - From point \( B \), draw another line that is tangent to the circle. This line will touch the circle at point \( B \) and will be perpendicular to the radius \( OB \). ### Step 5: Verify the Angle 5. **Verify the angle between the tangents**: - The angle between the two tangents \( AT \) and \( BT \) (where \( T \) is the point of tangency) should be \( 60^{\circ} \). ### Conclusion You have now constructed a circle of radius 5 cm and a pair of tangents to the circle such that the angle between them is \( 60^{\circ} \). If you need a visual representation or further assistance, please let me know!