# Angle Bisector Theorem

The Angle Bisector Theorem, a fundamental concept in geometry, explores the proportional relationships within a triangle when an angle bisector is introduced. According to this theorem, the angle bisector divides the opposite side into segments proportional to the adjacent sides, providing a mathematical foundation for understanding the distribution of lengths within triangles. This theorem not only serves as a crucial tool for geometric proofs but also finds practical applications in various fields, making it an indispensable element in the study and application of geometry.

Questions

- A triangle has corners at points A, B, and C. Side AB has a length of #21 #. The distance between the intersection of point A's angle bisector with side BC and point B is #7 #. If side AC has a length of #24 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #45 #. The distance between the intersection of point A's angle bisector with side BC and point B is #6 #. If side AC has a length of #42 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #16 #. The distance between the intersection of point A's angle bisector with side BC and point B is #12 #. If side AC has a length of #27 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #9 #. The distance between the intersection of point A's angle bisector with side BC and point B is #6 #. If side AC has a length of #15 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #15 #. The distance between the intersection of point A's angle bisector with side BC and point B is #9 #. If side AC has a length of #24 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #9 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #14 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #18 #. The distance between the intersection of point A's angle bisector with side BC and point B is #3 #. If side AC has a length of #20 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #6 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #8 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #15 #. The distance between the intersection of point A's angle bisector with side BC and point B is #5 #. If side AC has a length of #16 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #12 #. The distance between the intersection of point A's angle bisector with side BC and point B is #9 #. If side AC has a length of #11 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #12 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #9 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #9 #. The distance between the intersection of point A's angle bisector with side BC and point B is #6 #. If side AC has a length of #16 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #36 #. The distance between the intersection of point A's angle bisector with side BC and point B is #8 #. If side AC has a length of #42 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #36 #. The distance between the intersection of point A's angle bisector with side BC and point B is #14 #. If side AC has a length of #36 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #24 #. The distance between the intersection of point A's angle bisector with side BC and point B is #9 #. If side AC has a length of #35 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #15 #. The distance between the intersection of point A's angle bisector with side BC and point B is #7 #. If side AC has a length of #24 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #42 #. The distance between the intersection of point A's angle bisector with side BC and point B is #9 #. If side AC has a length of #45 #, what is the length of side BC?
- Please solve q 96 ?
- A triangle has corners at points A, B, and C. Side AB has a length of #12 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #8 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #48 #. The distance between the intersection of point A's angle bisector with side BC and point B is #8 #. If side AC has a length of #42 #, what is the length of side BC?