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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