Question

In a triangle $ABC$, D is a point on BC such that any point on AD is equidistant from the points B and C. Which of the following is necessarily true

• A. $AB=BC$
• B. $BC=AC$
• C. $AC=AB$
• D. $AB=BC=AC$

Answer 1

The correct option is C $AC=AB$

Given $D$ is any point on $BC$ and $AD$ is equidistant from $B$ and $C$, which means $D$ is the center of $BC$ and $\angle BAD=\angle CAD$.

This shows that $AB=CA$. However, $BC$ need not be equal to $AB$ or $AC$.