Question

now, the segments ( overline{kl} ) and ( overline{km} ) are tangent to the circle centered at ( o ). given that ( ol = 12 ) and ( km = 12.6 ), find ( ok ).

Explanation:

Step1: Use the property of tangent to a circle

A tangent to a circle is perpendicular to the radius at the point of tangency. So, \( \angle OLK = 90^{\circ}\). Also, by the property of tangents from an external point, \(KL=KM = 12.6\) (tangents from a common external point \(K\) to the circle are equal).

Step2: Apply the Pythagorean theorem

In right - triangle \(OLK\), by the Pythagorean theorem \(OK^{2}=OL^{2}+KL^{2}\). Given \(OL = 12\) and \(KL=12.6\), we substitute these values into the formula:

$$
LATEXBLOCK0
$$

Answer:

\(17.4\)