Three Dimensional Geometry Question 344
Question: Let A(4, 7, 8), B(2, 3, 4), C(2, 5, 7) be the vertices of a triangle ABC. The length of internal bisector of $ \angle A $ is
Options:
A) $ \frac{\sqrt{34}}{2} $
B) $ \frac{3}{2}\sqrt{34} $
C) $ \frac{2}{3}\sqrt{34} $
D) $ \frac{\sqrt{34}}{3} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ AB=6,BC=\sqrt{13,}CA=3 $
$ \therefore AB:AC=2:1 $ Internal bisector of an angle divides the opposite side in the ratio of adjacent sides
$ \therefore \frac{BD}{CD}=\frac{AB}{AC}=\frac{2}{1} $
$ \therefore $ Coordinate of D are $ ( 2,\frac{13}{3},6 ) $
$ \therefore $ Length $ AD=\frac{2}{3}\sqrt{34} $
BETA
