SATHEE: Quantitative Aptitude Ques 1344

Quantitative Aptitude Ques 1344

Question: Two circles of same radius 5 cm, intersect each other at A and B. If AB = 8 cm, then the distance between the centres is

Options:

A) 10 cm

B) 4 cm

C) 6 cm

D) 8 cm

Show Answer

Answer:

Correct Answer: C

Solution:

On joining AO and AP. In $ \Delta AOX, $ by Pythagoras theorem, $ AO^{2}=AX^{2}+OX^{2} $

$ \Rightarrow $ $ {{(5)}^{2}}={{( \frac{AB}{2} )}^{2}}+{{(OX)}^{2}} $

$ \Rightarrow $ $ 25={{( \frac{8}{2} )}^{2}}+{{(OX)}^{2}} $

$ \Rightarrow $ $ {{(OX)}^{2}}=25-16 $

$ \therefore $ $ OX=\sqrt{9}=3cm $ Similarly, in $ \Delta APX, $ $ PX=3cm $

$ \therefore $ Distance between the centre $ =OX+PX=3+3=6cm $ Alternate Method $ OA=AP=5cm $ [radius] $ AX=BX=\frac{AB}{2}=\frac{8}{2}=4cm $

$ \therefore $ $ OX=\sqrt{OA^{2}-AX^{2}}=\sqrt{{{(5)}^{2}}-{{(4)}^{2}}} $ $ =\sqrt{25-16}=3 $

$ \therefore $ $ OP=2\times OX=3\times 2=6cm $

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