Question

the radii of two concentric circles are 40cm and 41cm, what is the length of a chord of the bigger circle which is tangent to the smaller circle?​

Answer 1

Answer:

OC=40cm,OB=41cm

OC⊥AB since AB is tangent to the smaller circle .

⟹AC+BC

In △OCB

OB^{2}OB2 =OC^{2}OC2 +BC^{2}BC2

⟹BC^{2}BC2 =41^{2}412 -40^{2}402 =818×1

⟹BC=9cm

⟹AB=2BC=18cm

Hence the answer is 18cm

Step-by-step explanation:

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Answer 2

Let us the take the tangent as PQ and the centre of both the circles as O and OR as the radius of the smaller circle.

Given:

OR = 40cm

OQ= 41cm

Step-by-step explanation:

USING PYTHAGORAS THEOREM:

$ab {}^{2} + bc {}^{2} = ac {}^{2}$

40^2 + x^2 = 41^2

1600 + x^2= 1681

x^2 = 1681-1600

x^2= 81

x= √81

x= 9= QR

theorem: a chord drawn to the bigger concentric circle which is a tangent to the smaller concentric circle forms two congruent triangles.

thus, PQ= 2 QR

PQ= 2× 9

PQ= 18