Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.

Given: 

Radii of two co-centric circles.

To do: 

We have to construct a tangent of the circle with radius 4 cm from a point on the co-centric circle of radius 6 cm.

Solution:

Steps of construction:

1. Draw two concentric circle with centre O and radii 4 cm and 6 cm Take a point P on the outer circle and then join OP 

2. Draw the perpendicular bisector of OP. Let the bisector intersects OP at M 

3. With M as the center and OM as the radius, draw a circle. Let it intersect the inner circle at A and B.

4. Join PA and PB. 

Therefore, PA and PB are the required tangents. 

In $\triangle OAP$,

$OP^2=OA^2+AP^2$

$6^2=OA^2+4^2$

$OA^2=36-16$

$OA=\sqrt{20}$

$OA=2\sqrt5\ cm$

Similarly,

$OB=2\sqrt5\ cm$

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Updated on: 10-Oct-2022

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