If G is the circumcenter of triangle ABC, AG = 6x + 1, GC = 9x – 11, and BC = 38, find GF.

Mathematics

1 answer:

maks197457 [2]2 years ago

6 0

Answer:

GF = 16.25

Step-by-step explanation:

If G is the circumcenter of triangle ABC, AG = 6x + 1, GC = 9x – 11, and BC = 38, find GF.

Step 1

We find x

AG = GC

6x + 1 =9x - 11

Collect like terms

1 + 11 = 9x - 6x

12 = 3x

x = 12/3

x = 4

Step 2

We solve for AG

GC = 9x + 11

GC = 9(4) + 11

GC = 36 + 11

GC = 25

Step 3

Solving for GF, using Pythagoras Theorem

GF² + BG² = GC²

GF² = GC² - BG²

GF = √GC² - BG²

GF = √25² - 19²

GF = √264

GF = 16.248076809

GF = 16.25

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