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Draw a circle center O and radius 6 cm. Construct a pair of tangents from a point 10 cm a part of its center. Also measure the length of tangents drawn.

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Given : A circle center O and radius 6 cm. 

Also a point P at distance of 10 cm from the center of the circle.

Steps of construction :

(1) First of all we draw a circle with center O and radius 6 cm.

(2) Take a point P part of 10 cm from O. Join OP.

(3) Draw a perpendicular bisector of OP that intersects OP at M.

(4) Taking M as center and radius OM = OP. draw a circle which intersects the given circle at T1 and T2.

(5) Join PT1 and PT2 which are the required tangents.

Proof : We know that a tangent is the perpendicular on the point of contact.

∴ ∠OT1P = ∠OT2P = 90°

Now, Join OT1 and OT2, In the circle OT1, PT2 OP is diameter.

∴ ∠OT1P is the angle of semicircle.

∴ ∠OT1P = 90°

Similarly ∠OT2P = 90°

Hence, PT1 and PT2 are the tangents to the given circle.

On measuring, we get

PT1 = PT2 = 8.0 cm

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