In delta NML NL NM and the perimeter is 52 cm A B and C are

In delta NML, NL = NM, and the perimeter is 52 cm. A, B, and C are points of tangency to the circle. MC = 6 cm. Find NL. Explain your reasoning. (The figure is not drawn to scale.)

Solution

Given MC = 6 cm, NL = NM , Perimeter of triangle NML = 52 cm.

By the tangent properties, BM =CM, and BL = CL, also AL = CM

So, ML = BL + BM = 6 + 6 = 12 cm

So, in triangle NML, we have

ML + NL + NM = 52

12 + NL + NL = 52

2 NL = 52 - 12 = 40

NL = 40 /2 = 20

Therefore, NL = 20 cm