Browse · MATH
Printjmc
geometry senior
Problem
In acute triangle , altitudes , , and intersect at the orthocenter . If , , and , then find the length of .
Solution
By Pythagoras, , so .
Triangles and are right, and share , so they are similar. Hence, so Then .
Triangles and are right, and share , so they are similar. Hence, so Then .
Final answer
\frac{99}{20}