Question

In the above figure find the ratio between the $△$AOB and $△$COD, if $AB=3CD$.

Answer 1

Let $△AOB\sim △COD$.

We know that the arc of similar triangles are proportional to squares of their corresponding altitude, therefore with $AB=3CD$, we have,

$\frac{Ar(△AOB)}{Ar(△COD)}=\frac{A{B}^2}{C{D}^2}=\frac{(3CD{)}^2}{C{D}^2}=\frac{9C{D}^2}{C{D}^2}=\frac{9}{1}$

Hence, the ratio between the $△AOB$ and $△COD$ is $9:1$.