Question

O is the point in the exterior of $△ABC$.Use the symbols$<,>\text{or}=to$ make the following statements true.

$\mathrm{OB}+\mathrm{OC}>\mathrm{BC}$

Answer 1

Construction of figure;

$\mathrm{O}$ is the point in the exterior of $△\mathrm{ABC}$.

Join $\mathrm{OA},\mathrm{OB}\mathrm{and}\mathrm{OC}$.

Here, we can see $\mathrm{AOB}$ is a triangle.

We know that Triangle inequality theorem states that , Sum of the length of any two sides of a triangle is greater than the third side.

$\mathrm{OB}+\mathrm{OC}>\mathrm{BC}$

Hence, $\mathrm{OB}+\mathrm{OC}\underline{>}\mathrm{BC}$