Question

If $△ABC$ seg $AP$ is a median. If $BC=18,A{B}^2+A{C}^2=260$ Find AP.

• A. $5$
• B. $9$
• C. $7$
• D. $8$

Answer 1

The correct option is C $7$

$AP$ is median & $BP=PL=\frac{1}{2}BC=9units$

Why appollonius theorem, we have

$|AB{|}^2+|AC{|}^2=2(|1AP{|}^2+|BP{|}^2)$

we know $A{B}^2+A{C}^2=260$

& $260=2(A{P}^2+B{P}^2)$

$A{P}^2+q^2=130$

$A{P}^2=130-81$

$A{P}^2=49$

$AP=7units$