SOLUTION: 6. LM is a tangent drawn to circle O, JK=2, and LK=9. If MK is perpendicular to JL, what is the value of MK? 7. Given M<AEDA=35, mBC=30, and m<F=65, what is the mAC? https://docs

Algebra ->  Circles -> SOLUTION: 6. LM is a tangent drawn to circle O, JK=2, and LK=9. If MK is perpendicular to JL, what is the value of MK? 7. Given M<AEDA=35, mBC=30, and m<F=65, what is the mAC? https://docs      Log On


   

Question 1159929: 6. LM is a tangent drawn to circle O, JK=2, and LK=9. If MK is perpendicular to JL, what is the value of MK?
7. Given M https://docs.google.com/document/d/15YVcau3h66TYhBpf6IN_VtPFuIyLQgLV6d8C0IYgvYo/edit
Thank you very much and stay safe.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

JK=2
LK=9
MK+perpendicular to JL
MK=?
since MK and LK are legs of right triangle LKM, and ML is hypotenuse

first we need to calculate the length of ML using tangent secant rule
%28ML%29%5E2=LK%2ALJ................since LJ=LK%2BJK=9%2B2=11
%28ML%29%5E2=9%2A11
%28ML%29%5E2=99

then, use Pythagorean theorem to find MK :
%28MK%29%5E2=+%28ML%29%5E2-%28LK%29%5E2
%28MK%29%5E2=+99-81
%28MK%29%5E2=+18
MK=+sqrt%2818%29
MK=+sqrt%289%2A2%29
MK=3sqrt%282%29


Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
6. LM is a tangent drawn to circle O, JK=2, and LK=9. If MK is perpendicular to JL, what is the value of MK?
7. Given M https://docs.google.com/document/d/15YVcau3h66TYhBpf6IN_VtPFuIyLQgLV6d8C0IYgvYo/edit
Thank you very much and stay safe.
For # 6., you don't need to do anything that woman tells you.  It's way too UNNECESSARY. This is done as follows:

Δs MLK and MKJ are right-triangles, so they’re similar, and share a COMMON side, or both have a REFLEXIVE side, MK
We then get: matrix%281%2C3%2C+MK%2FKL%2C+%22=%22%2C+JK%2FMK%29
matrix%281%2C3%2C+MK%2F9%2C+%22=%22%2C+2%2FMK%29 ------ Substituting 9 for KL and 2 for JK
matrix%281%2C3%2C+%28MK%29%5E2%2C+%22=%22%2C+9%282%29%29 ------ Cross-multiplying

I wonder when she'll learn how to do math problems, and STOP confusing these people or making these problems so COMPLEX and time-consuming!
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For # 7., C is not shown. I can guess where it is, but I'd rather you make the entire graph viewable!