Question

mn is tangent to ⊙k. what is kn? n 5 yd m 12 yd k kn = yd submit work it out not feeling ready yet? these can 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, $\angle KMN = 90^{\circ}$, and triangle $KMN$ is a right - triangle with $KM$ as the radius, $MN$ as the tangent, and $KN$ as the hypotenuse.

Step2: Apply Pythagorean theorem

In right - triangle $KMN$, by the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 5$ (length of $MN$), $b = 12$ (length of $KM$), and $c$ is the length of $KN$. So, $KN=\sqrt{5^{2}+12^{2}}$.

Step3: Calculate the value of $KN$

$KN=\sqrt{25 + 144}=\sqrt{169}=13$.

Answer:

13