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.

Answer 1

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.