# Triangle geometry with bisectors

In triangle $$ABC$$, $$AB=10$$, $$CA=12$$. The bisector of ∠B intersects $$CA$$ at $$E$$, and the bisector of ∠C intersects $$AB$$ at $$D$$.

$$AM$$ and $$AN$$ are the perpendiculars to $$CD$$ and $$BE$$ respectively. If $$MN=4$$, then how can I find $$BC$$?

Thank you!

• Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This post will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – ExtremeRaider May 14 at 12:11
• Whats your effort in this question. Did you tried it – Vedant Chourey May 14 at 12:14
• math.stackexchange.com/questions/3221915/… – CY Aries May 14 at 13:20
• The tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, use MathJax. – dantopa May 16 at 1:59