Plane trigonometry, by S.L. Loney.

240

TRIGONOMETRY.

Hence, by addition, we have
b2 + c2 = 2x2 + -
2
AD = x = 2b2 + 2c2 - a2.
Hence also AD = V/b2 + c2 + 2bc cos A (Art. 164).
So also
BE= 2 V/2c2 + 2a2 - b2, and CF = ^2a2 + 2b2 - c2.
214. Angles that the median AD makes with the sides.
If the z BAD = 3, and z CAD = y, we have
sin 7 DC a
sin C- AD 2x'
a sin C a sin C.'. sinmy=.
2x!/2b2 + 2c2 - a2
a sin B
Similarly sin = a sin B
V2b2 + 2c2 - a2
Again, if the z ADC be 0, we have
sin 0 AC b
sin C AD x
b sin C 2b sin C
sin 0= =
x /2b2 + 2C2 _ a2
The angles that AD makes with the sides are therefore
found.
215. The centroid lies on the line joining the circumcentre to the orthocentre.