Draw a circle of radius 6cm. draw a tangent to the circle making 30degree with the line passing through the centre. measure the lenght of the tangent.

Can someone plz tell me the steps of construction to do this??

Dear Student!

Follow the given steps to construct a tangent to the circle.

Step1: Take a point O and draw a circle of radius, OA = 6 cm.

Step2: Produce OA to B such that OA = AB = 6 cm

Step3: Taking A as centre, draw a circle of radius AD = AB = 6 cm. Let it intersect the circle in P.

Step4: Join BP

**BP is the required tangent to the circle.**

OA = OP (Radius of circle with centre O)

AP = OP (Radius of circle with centre A)

∴ OA = OP = AP

Hence, ΔOAP is an equilateral triangle.

∴ ∠OAP = ∠AOP = ∠OPA = 60°

OP ⊥ PB (Radius is perpendicular to tangent at the point of contact)

∴ ∠OPB = 90°

In ΔOBP

∠BOP + ∠OBP + ∠OPB = 180°

∴ 60° + ∠OBP + 90° = 180°

**⇒ ∠OBP = 180° – 150° = 30°**

Length of tangent, PB =

Thus, the length of the tangent, PB is cm.

Cheers!

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