Steps to construct the required figure:
Step 1:Draw a circle of radius 5 cm and mark the center as O.
Step 2: As we have angle between the tangents as 60°
\(\therefore \) By quadrilateral property we have angle between the radii of circle is 120°
Step 3:Draw two radius OA and OB such that they have angle of 120°
Step 4:At points A and B, draw 90°angles and mark the point P where the arms of these angles intersect.
Step 5:we get PA and PB as our required tangents.
Since, OA is the radius , so PA has to be a tangent to the circle.
Similarly, PB is the tangent to the circle.
\(\angle APB=360° - \angle OAP - \angle OBP - \angle AOB \)
= 360° - 90° - 90° - (180° - 60°)
= 360° – 360° +60° = 60°
Thus the tangents PA and PB are inclined to each other at an angle of 60°