Question

In $△ABC,AB=BC=6$ cm. $A$ 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 $△ABC$?

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

Answer 1

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

Given in
$△ABC$,
$AB=BC=6$ cm

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

In $△ABC$ and $△EBD$,

$\frac{BE}{AB}=\frac{BD}{BC}=\frac{2}{6}=\frac{1}{3}$