Question

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the
larger circle which touches the smaller circle.
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Answer 1

Answer:

Let two concentric circle with centre O have radii OQ =5cm and OM=3cm ,where PQ is a chord of larger circle and tangent to the smaller circle at M the point of contact

OM perpendicular to PQ

angle OMQ=90°

In right ΔOMQ by Pythagoras theorem ,we have

MQ=√OQ^2 -OM^2

=√5^2 -3^2

=√25-9

=√16

=4cm...

PQ=2•MQ

=2•4

=8 cm..........

Answer 2

ANSWER

Let O be the centre of the concentric circle of radii 5 cm and 3 cm respectively. Let AB be a chord of the larger circle touching the smaller circle at P.

Then

AP=PB and OP⊥AB

Applying Pythagoras theorem in △OPA, we have

OA ^2 =OP^ 2 +AP^ 2

⇒25=9+AP ^2

⇒AP^ 2 =16

⇒AP=4 cm

∴AB=2AP=8 cm

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