Question 1210193: Triangle ABC has AB = 6. Let D lie on BC such that \overline{AD} bisects \angle BAC. If BD = 3 and CD = 5, what is CD?
Found 3 solutions by CPhill, ikleyn, greenestamps:
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! You've already stated that CD = 5 in the problem. It seems there might be a typo, and you intended to ask for something else, such as the length of AC.
Let's solve for AC, assuming that's what you meant to ask.
**1. Angle Bisector Theorem**
The Angle Bisector Theorem states that if AD bisects angle BAC in triangle ABC, then:
AB/AC = BD/CD
**2. Plug in the Given Values**
* AB = 6
* BD = 3
* CD = 5
6/AC = 3/5
**3. Solve for AC**
* Cross-multiply: 3 * AC = 6 * 5
* 3 * AC = 30
* AC = 30 / 3
* AC = 10
**Therefore, if the question was to find AC, the answer is AC = 10.**
**If you intended to ask another question about CD, please clarify and I'll be happy to help.**
Answer by ikleyn(52903)  (Show Source):
You can put this solution on YOUR website! .
Triangle ABC has AB = 6. Let D lie on BC such that \overline{AD} bisects \angle BAC.
If BD = 3 and CD = 5, what is CD?
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Hello, in your post, the question is "what is CD ?"
But in the problem's description, CD is given directly and explicitly: "CD =5".
So, your post is, obviously, DEFECTIVE.
It needs to be fixed/repaired/edited, so as not to look too stupid.
An attentive well-wisher, @ikleyn, smiling.
Answer by greenestamps(13215)  (Show Source):
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