Point f is on circle c.

what is the length of line segment gf?

12.5 units
15.0 units
17.5 units
20.0 units

Length of GF is 20 units

Length of EG = 10 unit

Length of EC = 7.5 unit

Length of GF

Length of GF = Length of GC + Length of CF

Length of GF = √EG² + EC² + 7.5

Length of GF = √10² + 7.5² + 7.5

Length of GF = √156.25 + 7.5

Length of GF = 12.5 + 7.5

Length of GF = 20 units

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Answer

Find out the length of line segment GF .

To prove

In Δ GEF is a right triangle .

As shown in the diagram

GE = 10 units

EC = 7.5 units

By using the pythagorean theorem

Hypotenuse² = Perpendicular² + Base²

GC² = GE² + EC²

      =  10² + 7.5²

      = 100 + 56.25

      = 156 .25

GC = 12 .5 units

As shown in the diagram

CF is the radius of a circle .

CF = 7.5 units (As in the figure EC = 7.5 units)

GF = GC + CF

       =  12 .5 units + 7.5 units

      =  20 units

Therefore option (d) is correct .

Hence proved