Question

mn is tangent to ⊙k. what is kn? 8 km 15 km kn = km submit work it out not feeling ready yet? these pythagorean theorem (100) lesson: tangent to a circle

Explanation:

Step1: Recall tangent - radius property

A tangent to a circle is perpendicular to the radius at the point of tangency. So, $\triangle{KMN}$ is a right - triangle with $\angle{KMN}=90^{\circ}$, $KM = 15$ km (radius) and $MN = 8$ km.

Step2: Apply Pythagorean theorem

In right - triangle $\triangle{KMN}$, by the Pythagorean theorem $KN^{2}=KM^{2}+MN^{2}$. Substitute $KM = 15$ and $MN = 8$ into the formula: $KN^{2}=15^{2}+8^{2}=225 + 64=289$.

Step3: Solve for $KN$

Take the square root of both sides. Since $KN>0$, $KN=\sqrt{289}=17$ km.

Answer:

17