Given :circle centre D. DE is perpendicular to FG, cutting FG at M. FG =24 units, EM =8 units and MD =x units. calculate the length of the radius FD.
To find the length of the radius FD, we first need to find the length of DE using the Pythagorean theorem.
By Pythagorean theorem on triangle DEM:
DE^2 = EM^2 + MD^2
DE^2 = 8^2 + x^2
DE^2 = 64 + x^2
Since DE is the radius FD, we can write DE as FD.
FD^2 = 64 + x^2
Since FD is the radius of the circle with center D, FD is perpendicular to FG, and M is the midpoint of FG, FD is the perpendicular bisector of FG. This means that FM = MG = FG/2 = 24/2 = 12 units.
We can now find x by applying the Pythagorean theorem on triangle FDM:
FD^2 = FM^2 + MD^2
FD^2 = 12^2 + x^2
FD^2 = 144 + x^2
Now equate the two expressions for FD^2:
64 + x^2 = 144 + x^2
64 = 144
x^2 = 144 - 64
x^2 = 80
Now, we can calculate the length of the radius FD:
FD^2 = 144 + 80
FD^2 = 224
FD = √224
FD = 14.97 units
Therefore, the length of the radius FD is approximately 14.97 units.