Question

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

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

Answer 1

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


Given in $\Delta ABC,$
$AB=BC=6cm$

If a circle is drawn with $B$ as center and a radius of $2cm$,
it intersects $\Delta ABC$ at $2$ points, i.e., $D$ and $E$ (say).
$\Rightarrow BD=BE=2cm$ (radius of the same circle)

In $\Delta ABC$ and $\Delta EBD$,
$\frac{BE}{AB}=\frac{BD}{BC}=\frac{2}{6}=\frac{1}{3}$