Question

In the figure above, $AC=6$ and $BC=3$. Point $P$ (not shown) lies on $AB$ between $A$ and $B$ such that $CP\perp AB$. Which of the following could be the length of $CP$?

• A. $2$
• B. $4$
• C. $5$
• D. $7$
• E. $8$

Answer 1

The correct option is A $2$

$CP$ will create two right triangles, $ABP,BPC$ with hypotenuses $AC$ and $BC$. $CP$ will be a leg of both of those triangles, which means it will have to be shorter than either hypotenuse. The only choice that's shorter than $3$ is $2$.