SOLUTION: Angle C is the right angle. In right △ABC with right ∠C, AD bisects ∠BAC. Suppose that AC = 12 and DC = 6. Let BD = x. Then AB = 2x. Write the length of BC as an expressi

Question 1193847: Angle C is the right angle. In right △ABC with right ∠C, AD bisects ∠BAC.
Suppose that AC = 12 and DC = 6.
Let BD = x. Then AB = 2x. Write the length of
BC as an expression involving x
Use the Pythagorean Theorem to find x. Find BD and AB.
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!

What you have described is impossible. With the given measurements, it is not possible for AD to bisect angle BAC. That doesn't have anything to do with deriving the answers you need, but it is extraneous BS you shouldn't have included with the problem.

If BD measures

and DC measures 6, then BC must measure

. Then AB is the hypotenuse, so:

So just simplify and solve the quadratic for

to get BD, and then calculate

to get AB.

Hint: The quadratic factors. Second hint: One of the roots is negative, so discard it because a negative length for a line segment is absurd.

John

My calculator said it, I believe it, that settles it

From
I > Ø

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