draw a pair of tangents to a circle of radius 5cm which are inclined to each other at an angle of 60 degrees

Steps of Construction:

Step 1: Draw a circle with centre O and radius 5 cm.

Step 2: Take a point O’ on circle and join it to O.

Step 3: Extend OO’ to O’P such that O’P = OO’ = 5 cm.

Step 4: Take O’ as a centre and O’O as a radius and draw a circle whichintersects the previous circle at points A and B.

Step 5: Join P to A and P to B.

These are the required tangents that make an angle of 60° with each other.

Since, AO = OO’= AO’ (These all are the radius of circles)

So AO’O is an equilateral triangle.

O’ = O = A = 60°.

PO’A = 120°(Linear Pair angle)

And O’AP = 30° (PAO = 90°)

InPAO’

APO + O’AP + PO’A = 180°

APO = 30°

BPO = 30°

(A line between two tangents from the same point on a circle bisects the angle between them)

 APB = 60°.

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