Question

Which one of the following formula is used to find apollinius theorem for isosceles triangle?

• A. $a^2+b^2=2m^2+{\frac{c}{2}}^2$
• B. $b^2=m^2+{\frac{c}{4}}^2$
• C. $b^2+b^2=2m^2+{\frac{c}{2}}^2$
• D. $a^2+b^2=2m^2+{\frac{b}{2}}^2$

Answer 1

Answer: (B)

$b^2=m^2+{\frac{c}{4}}^2$

In any triangle, the sum of the squares on any two sides is equal to twice the square on half the third side together with twice the square on the median which bisects the third side.
Apollinius theorem formula,
$a^2+b^2=2[m^2+{\frac{c}{2}}^2]$
When the given triangle is isosceles, than $b=a$.
So, $b^2=m^2+{\frac{c}{4}}^2$ is the formula used for isosceles triangle.