Draw a circle of circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60°. Also justify the construction, Measure the distance between the centre of the circle and the point of intersection of tangents.

Steps of construction

1. Draw a circle of radius OA=4 cm.

2. Produce OA to B such that OA=AB=4 cm,

3. A as the centre draw a circle of radius AO=AB=4 cm. Suppose it cuts the circle drawn in step 1 at P and Q.

4. Join BP and BQ to get desired tangents.

In ∆OAP,

OA=OP=4 cm

[ Radius]

Also,

AP=4 cm

[ Radius of circle with center A]

∴ ∆OAP is equilateral

⇒ ∠PAO=60°

⇒ ∠BAP=120°

In ∆BAP,

BA=AP and ∠BAP=120°

∴ ∠ABP= ∠APB=30°

⇒ ∠PBQ=60°

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