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  • If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is (A) 3 cm (B) 6 cm(C) 9 cm (D) 1 cm

If the radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is
(A) 3 cm                      (B) 6 cm                      (C) 9 cm                      (D) 1 cm

Answers (1)

Answer (B) 6 cm
Solution
According to question

Here A is the center AB = 4 cm radius of small circle and AD = 5 cm radius of large circle. 
We have to find the length of the CD
\DeltaABD is a right-angle triangle.
 Hence use Pythagoras' theorem in \DeltaABD
\left ( AD \right )^{2}= \left ( AB \right )^{2}+\left ( BD \right )^{2}
\left ( 5 \right )^{2}= \left ( 4 \right )^{2}+\left ( BD \right )^{2}
25-16= \left ( BD \right )^{2}
BD= \sqrt{9}= 3
BD= 3cm
CD= CB+BD
CD= CB+BD
CD= BD+BD= 2BD\; \; \left ( \because CB= BD \right )
CD= 2\times 3= 6cm
CD= 6cm
Hence the length of the chord is 6 cm.



              

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infoexpert27

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