Draw a circle of radius 3 cm. Draw a tangent to the circle making an angle of 30° with a line passing through the centre.
HINT: Draw a circle with centre O and radius 3 cm. Draw a radius OA and produce it to B. Make ∠AOP = 60^o. Draw PQ ⊥ OP, meeting OB at Q. Then, PQ is the desired tangent such that ∠OQP = 30°.

Question

Draw a circle of radius 3 cm. Draw a tangent to the circle making an angle of 30° with a line passing through the centre.
HINT: Draw a circle with centre O and radius 3 cm. Draw a radius OA and produce it to B. Make ∠AOP = 60^o. Draw PQ ⊥ OP, meeting OB at Q. Then, PQ is the desired tangent such that ∠OQP = 30°.

Philoid · Accepted Answer

Steps of Construction:

1. Draw a circle with radius 3 cm and center A.

2. Draw diameter CD passing through A.

3. Draw ∠ CAE = 60° such that AE is a radius of the circle with the point E lying on the circle.

4. Extend the diameter DC to G.

5. Draw FE perpendicular to AE such that FE intersects the DG at F.

Thus, FE is the required tangent with ∠ EFA = 30°.