If in a `!ABC` ,CD is the bisector of `angleACB,` then CD =

Options

A. `(a+b)/(2ab)cosC/2`
B. `(a+b)/(ab)cosC/2`
C. `(2ab)/(a+b)cosC/2`
D. `(bsinA)/(sin(B+C/2))`

Explanation

To find the length of the angle bisector \( CD \) in triangle \( ABC \) where \( CD \) bisects \( \angle ACB \), we can use the Angle Bisector Theorem and some properties of triangles. Here’s the step-by-step solution:

### Step 1: Understand the Angle Bisector Theorem
The Angle Bisector Theorem states that the ratio of the lengths of the two segments created by the angle bisector is equal to the ratio of the lengths of the other two sides of the triangle. In triangle \( ABC \), if \( CD \) is the bisector of \( \angle ACB \), then:
\[ \frac{AD}{DB} = \frac{AC}{BC} \]
Let \( AC = b \) and \( BC = a \).
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