Question

If ML = 17 and MJ = 34 and KL = 8, find MK

Answer 1

Answer: MK = 15

Having that line KN is tangent to both circles, and point L being the center of circle L, we know that triangle KLM is a right triangle. Now, given that:

ML = 17

KL = 8

We can find MK through the Pythagorean theorem.

`ML^2=KL^2+MK^2`
`MK^2=ML^2-KL^2`
`MK^{}=\sqrt[]{ML^2-KL^2}`
`MK=\sqrt[]{17^2-8^2}`
`MK=\sqrt[]{289-64}`
`MK=\sqrt[]{225}`
`MK=15`

Therefore, MK = 15