RRB Technician 2014 Ques 4
Question: AB and CD are two chords of a circle such that $ AB=10 $ cm, $ CD=24cm $ and $ AB||CD $ . The distance between AB and CD is 17 cm. Then, the radius of the circle is equal to
Options:
A) 13cm
B) 169 cm
C) 26 cm
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- Let radius be r, then In $ \Delta OMD,,r^{2}=OM^{2}+MD^{2} $ $ r^{2}=12^{2}+x^{2} $ ?..(i) In $ \Delta OLB,r^{2}=LB^{2}+OL^{2} $ $ r^{2}={{(17-x)}^{2}}+5^{2} $ …(ii) Comparing of both equations, $ 12^{2}+x^{2}={{(17-x)}^{2}}+25 $ $ 43x=170\Rightarrow x=\frac{170}{34}=5 $ and $ r^{2}=12^{2}+5^{2} $ $ =144+25=169 $
$ \therefore $ $ r=13,cm $
BETA
