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IOQM P22 2024

Source:

September 8, 2024
geometryquadratic formulatrigonometry

Problem Statement

In a triangle ABCABC, ∠BAC=90∘\angle BAC = 90^{\circ}. Let DD be the point on BCBC such that AB+BD=AC+CDAB + BD = AC + CD. Suppose BD:DC=2:1BD : DC = 2:1. if ACAB=m+pn\frac{AC}{AB} = \frac{m + \sqrt{p}}{n}, Where m,nm,n are relatively prime positive integers and pp is a prime number, determine the value of m+n+pm+n+p.
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