# Draw a circle at radius 3 cm Take a point at 5.5 cm from the centre at the circle.

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Draw a circle at radius 3 cm. Take  a point at 5.5 cm from the centre at the circle. From point P, draw two tangent to the circle.

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Steps of construction :

(i) Take a point O in the plane paper and draw a circle of radius 3 cm.

(ii) Mark a point P at distance 5.5 cm from the centre O and OP. (iii) Draw the right bisector at OP, intersecting OP at Q.

(iv) Taking Q as the centre and OQ = PQ as radius, draw a circle to intersect the given circle at T and T’.

(v) Join PT and PT’ to get the required tangent.

Type (II). Construction of a tangent to a circle from an external point when its centre is known.

Steps of construction :

Let P be the external point from where the tangent are to be drawn to the given circle.

(i) Through P draw a secant PAB to intersect the circle at A and B. (ii) Join AP to a point C such that AP = DX is equal to the mid-point at AC.

(iii) Draw a semi-circle with BC as diameter.

(iv) Draw PD ⊥ BCX intersecting the semi-circle at D.

(v) With P as centre and PD as radius draw arcs to intersect the given circle at T and T’.

(vi) Join PT and PT’. Then PT and PT’ are the required tangent.