Math, asked by rp5387701, 7 months ago

two concentric circles of radii 5cm and 3cm ​

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Answers

Answered by Anonymous
60

\: \: \: \: \: \: \: \: \star\bf\: \: \: {Required\: figure}

Given

  • Radius of smaller circle = 3cm
  • Radius of larger circle = 5cm

To find

  • Length of chord of the larger circle.

Solution

  • According to the figure, we need to find the length of PQ.

As we can see that OAP is a right angled triangle.

  • Therefore, in triangle OAP.

\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{By\: using\: Pythagoras\: theorem}}}

\tt:\implies\: \: \: \: \: \: \: \: {OP^2 = OA^2 + AP^2}

\tt:\implies\: \: \: \: \: \: \: \: {(5)^2 = (3)^2 + AP^2}

\tt:\implies\: \: \: \: \: \: \: \: {25 = 9 + AP^2}

\tt:\implies\: \: \: \: \: \: \: \: {AP^2 = 25 - 9}

\tt:\implies\: \: \: \: \: \: \: \: {AP^2 = 16}

\tt:\implies\: \: \: \: \: \: \: \: {AP = \sqrt{16}}

\tt:\implies\: \: \: \: \: \: \: \: {AP = 4\: cm}

  • As we can see in the figure, that OA is the perpendicular bisector of PQ.

\star{\boxed{\sf{\orange{PQ = 2AP}}}}

\tt\longrightarrow{PQ = 2 \times 4}

\tt\longrightarrow{PQ = 8\: cm}

Therefore,

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

Hence,

  • Option (c) is the correct option.
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Anonymous: Well explained !
Answered by Anonymous
9

★Given that,two concentric circles are of radii 5cm and 3cm.

To Find:- length of the chord of the larger circle, (in cm), which touches the smaller circle is.?

__________________________________________

solution:

now,let the radius of the bigger circle be R and the radius of the smaller circle be r

as it is given that R= 5cm = OB and r = 3cm= OD

and AB is the chord whose length is to be found.

AB=BD and OD AB

therefore,triangle OBD is right angled.

where, OD²+BD²=OB²

 ⟼{3}^{2}  +  {bd}^{2}  =  {5}^{2}  \\ ⟼9 +  {bd}^{2}  = 25cm \\ ⟼ {bd}^{2}  = 25 - 9 cm\\ ⟼ {bd}^{2}  = 16cm \\ ⟼ \sqrt{bd}  = 4cm \\ ⟼db = \mathbb{\boxed{\purple{4cm}}\star}

Since, AD= BD=4cm

therefore ,AB=AD+BD

⇒AB= 4+4cm

⇒AB=\mathbb{\boxed{\purple{8cm}}}

hence option c 8cm is correct.!

hope this helps.!!

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