1)Draw in radii OK and JK. Since and are radii of the same circle, they are . This means that OK = 12. Add the length of OK to the diagram. Step 2: Radii and are perpendicular to because of the radius-tangent theorem. By definition of perpendicular, angles KOM and LNM are right angles. This means that triangles KOM and LNM are right triangles. Angle LMN is common to both right triangles, so by the , triangles KOM and LNM are similar. Step 3: Let LM = x. We know the lengths of the radii of each circle, so KL = 12 + 8 = 20. Add the length of KL to the diagram. Step 4: By the definition of similar polygons, the lengths of corresponding sides are . This means that .