Question

Draw 2 consistent circles of radii 4cm and 6.5cm . Then taking a point on the outer circle construct the pair of tangents to the other . Also , measure the lengths of the tangents

Answer 1

STEP-BY-STEP SOLUTION

(1)Draw two concentric circle C

1

and C

2

with common center

0 and radius 4cm and 6cm

(2) Take a point P on the outer circle C

2

and join OP.

(3) Draw the bisector of OP which bisect OP at M'.

(4) Taking M' as center and OM' as radius draw a dotted circle which

cut the inner circle C

1

at two point M and P.

(5) Join PM and PP'. Thus, PM and PP' are required tangent.

On measuring PM and PP'.

PM=PP

′

=4cm

Bycalculation:

InΔOMP,∠PMO=90

0

PM

2

=OP

2

−OM

2

(by pythagoras theorem)

PM

2

=(6)

2

−(4)

2

=38.5−16=22.5

PM

2

=

PM=

22.5cm

=4.74cm

Hence,

the length of the tangent is 4.74cm

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