Question 198
Let $ABC$ be an isosceles triangle with $|AB| = |AC|$. If $D$ is a point on the circumcircle of $\triangle ABC$ on the same side of $BC$ as $A$, prove
$$
| AB | + | AC | \ge | DB | + | DC |
$$
with equality if and only if $D = A$. Hence prove, of all triangles described in a circle, the equilateral triangle has the greatest perimeter.
$$
| AB | + | AC | \ge | DB | + | DC |
$$
with equality if and only if $D = A$. Hence prove, of all triangles described in a circle, the equilateral triangle has the greatest perimeter.