Steps of Construction:
Step I: Draw a circle with centre O and radius 3 cm.
Step II: Draw any diameter AOB.
Step III: Draw a radius OC such that ∠ BOC = 60°.
Step IV: At C, we draw CM ⊥ OC and at A, we draw AN ⊥ OA.
Step V: Let the two perpendiculars intersect each other at P.
Then, PA and PC are required tangents.
Justification:
Since OA is the radius, so PA has to be a tangent to the circle. Similarly, PC is also tangent to the circle.
∠APC = 360° – (∠OAP + ∠OCP + ∠AOC)
= 360° – (90° + 90° + 120°) = 360° – 300° = 60°
Hence, tangents PA and PC are inclined to each other at an angle of 60°.
