Question

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.

Answer 1

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