If I have triangle ABC with side lengths a,b,c, and



Answered question


If I have triangle ABC with side lengths a,b,c, and I have an angle bisector coming out of point A, which divides side a into two sections at intersection point P, what is the length of BP and PC?

Answer & Explanation



Beginner2022-06-27Added 22 answers

This is well known property of bisector. B P C P = A B A C . So you have a system
B P C P = b c and B P + P C = a
The solution to the system is B P = a c b + c and C P = a b b + c


Beginner2022-06-28Added 10 answers

You have enough information to solve each of the two triangles you get. For example, for Δ A B P, you have the angles 1 2 A and B, and the side b. Probably the easiest approach is to find the third angle (using angle-sum= 180 ) and then use the law of sines.

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