Points B and D are points of tangency. Find the two possible lengths of AB.

Question

anonymous · Answer

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anonymous · Answer

I already have 14. I just don't know the second possible length.

campbell_st · Answer

well i don't know how you got 14

what you do need to know is that tangents from an external point are equal in length. 

this means that

$$x^2 +x -6 = x +10$$

all you need to do is solve for x. 

hope it helps

anonymous · Answer

I got 4 for one x. Which would mean AB=14. @campbell_st

campbell_st · Answer

well you should have found that 

$$x^2 = 16$$

so 

$$x = \pm 4$$

substitute the 2 values for x

x = 4   and you get 14

what about 

x = -4   what do you get...?

anonymous · Answer

-4^2+-4-6=-26
-4+10=6

anonymous · Answer

@campbell_st

campbell_st · Answer

well you have a slight error in your calculations 

$$(-4)^2 +(-4) - 6 = 16 - 4 - 6 = 6$$

you squared a negative and left it as a negative... it should be a postive

anonymous · Answer

So, when you square a negative it turns into a positive? @campbell_st

campbell_st · Answer

that's correct... its an error caused by calculators not knowing if the negative is an operator or a value... 

so always square negative number by putting them in brackets then squaring...

anonymous · Answer

Okay, I get it now! Thanks (: