Question

two concentric circles are of radii 5cm And 3 cm find the length of the chord of the larger circle which touches the smaller circle
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Answer 1

Question:-

Two concentric circles are of radii 5cm And 3 cm find the length of the chord of the larger circle which touches the smaller circle?

Method Of Solution:-

Let the two concentric circles with centre O.

Given:-

AB be the chord of the larger circle which touches the smaller circle at point P. 

Using Theorem 1(Tangent theorem)

∴ AB is tangent to the smaller circle to the point P.

Hence,

OP ⊥ AB

By Pythagoras theorem in ΔOPA,

OA² =  AP² + OP²
 = ) 5² = AP² + 3²
= ) AP2 = 25 - 9
= ) AP = 4

Here,

In ΔOPB,

Since OP ⊥ AB

AB = PB

AB =2AP

AB=2 × 4

= )8 cm

Hence,
‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎The length of the chord of the larger circle is 8 cm;-
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Answer 2

OA² =  AP²+ OP²

  5² = AP² + 3²


=) AP2 = 25 - 9

AP = 4

ACCORDING TO THE QUESTION



AB = PB

AB =2AP

AB=2 × 4

= 8 cm



‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎The length of the chord of the larger circle is 8 cm.
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