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SVEN [57.7K]
3 years ago
8

Common Tangents and AAA theorems

Mathematics
1 answer:
lubasha [3.4K]3 years ago
5 0
You know from similar triangles that ...
  KM/KO = LM/LN
  (20 +x)/12 = x/8
Multiplying by 24, we get
  2(20 +x) = 3x
  40 +2x = 3x
Subtracting 2x, we get
  40 = x . . . . . . . . . . the measure of LM

The Pythagorean theorem tells us
  (LN)² +(NM)² = (LM)²
Substituting known values, this becomes
  8² +(NM)² = 40²
  (NM)² = 40² -8² = 1600 -64 = 1536
Then the measure of NM is ...
  NM = √1536 ≈ 39.19

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