Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.

Given, two concentric circles of radii 3 cm and 5 cm with center O. We have to draw a pair of tangents from point P on outer circle to the other.

Steps of construction

1. Draw two concentric circles with center O and radius 3 cm and 5 cm.

2. Take any point P on the outer circle. Join OP.

3. Bisect OP, let M’ be the mid-point of OP.

Taking M’ as a centre and OM’ as radius draw a circle dotted which cute the inner circle at M and P’.

4. Join PM and PP’. Thus, PM and PP’ are required tangents.

5. On measuring PM and PP’, we find that PM=PP’=4 cm.

In ∆OMP,

∠PMQ=90°

∴ PM^{2}=OP^{2}=4cm

PM^{2}=(5)^{2}-(3)^{2}=25-9=16

PM = 4 cm

Hence, the length of both tangents is 4 cm.

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