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# Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°

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.

JUSTIFICATION:

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°