If line AD = 11 cm and line AB = 25 cm, calculate the length of line AC.

Question

anonymous · Answer

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anonymous · Answer

The secant-tangent rule is (whole secant) * (external part) = tangent^2. Therefore, to find the length of AC, you need to solve the equation $$AC*AD = AB^2$$

anonymous · Answer

I think I'm doing something wrong. The answer I got was 22.45.

anonymous · Answer

Can you run by your math step by step?

anonymous · Answer

That is your error. It's 11*x not 11+x and 25^2, not just 25

anonymous · Answer

Okay, here's my step-by-step.
1. (11 + CD) 11 = 25 squared
2. 121 + 11CD = 625
3. CD = 45.82. 
Alright, I see I made a mistake on my last calculation. But 45.82 isn't one of my options for an answer. Any thoughts?

anonymous · Answer

You don't need to separate AC into AD and DC, all you need to do is $$AC*11 = 625$$ $$AC = 56.8$$

anonymous · Answer

Oh! Thanks for the clarification. That helps a lot!

anonymous · Answer

AD*AC = AB^2

anonymous · Answer

x=56.8

anonymous · Answer

11*x=625
so x=56.81

anonymous · Answer

That looks right.