Question

In $\Delta ABC,AB=BC=6cm$. A circle is drawn with center at B and radius 2 cm. What is the scale factor of the triangle formed by the point B and the points where the circle intersects $△ABC$?

• A. $\frac{2}{3}$
• B. $1$
• C. $\frac{1}{3}$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $\frac{1}{3}$


Given in $\Delta ABC,AB=BC=6cm$.
If a circle is drawn with B as center and 2 cm radius,
it intersects $\Delta ABC$ at 2 points D and E.
$BD=BE=2cm$.
In $\Delta ABCand\Delta EBD$,
$\frac{BE}{AB}=\frac{BD}{BC}=\frac{2}{6}=\frac{1}{3}and\angle EBD=\angle ABC$.
By SAS similarity, $\Delta ABC$ and $\Delta EBD$
are similar.
The scale factor for the $\Delta EBD$
with respect to $\Delta ABC$ is $\frac{1}{3}$.