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 $
BETA
