A) \[{{a}^{2}}=2{{b}^{2}}\]
B) \[{{b}^{2}}=3{{a}^{2}}\]
C) \[{{b}^{2}}=2{{a}^{2}}\]
D) \[{{a}^{2}}=3{{b}^{2}}\]
Correct Answer: D
Solution :
We know altitude of equilateral \[\Delta ABC\]is \[\frac{\sqrt{3}}{2}a.\] \[\therefore \]Length of \[OC=\frac{\sqrt{3}}{2}a\times \frac{2}{3}=\frac{a}{\sqrt{3}}=\]radius Also, \[DF=b\] \[\Rightarrow \] \[DE=\frac{b}{2}\] In \[\Delta ODE,\]\[\cos 60{}^\circ =\frac{DE}{OD}=\frac{b/2}{a/\sqrt{3}}\] \[\Rightarrow \] \[\frac{1}{2}=\frac{\sqrt{3}b}{2a}\] \[\Rightarrow \] \[a=\sqrt{3}b\]\[\Rightarrow \]\[{{a}^{2}}=3{{b}^{2}}\]You need to login to perform this action.
You will be redirected in
3 sec